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Wyświetlanie 1-15 z 23
Tytuł:
Corona theorem for strictly pseudoconvex domains
Autorzy:
Gwizdek, Sebastian
Powiązania:
https://bibliotekanauki.pl/articles/2048987.pdf
Data publikacji:
2021
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Banach algebra
uniform algebra
Arens product
Gleason part
band of measures
representing measures
Opis:
Nearly 60 years have passed since Lennart Carleson gave his proof of Corona Theorem for unit disc in the complex plane. It was only recently that M. Kosiek and K. Rudol obtained the first positive result for Corona Theorem in multidimensional case. Using duality methods for uniform algebras the authors proved “abstract” Corona Theorem which allowed to solve Corona Problem for a wide class of regular domains. In this paper we expand Corona Theorem to strictly pseudoconvex domains with smooth boundaries
Źródło:
Opuscula Mathematica; 2021, 41, 6; 843-848
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Description of the scattering data for Sturm-Liouville operators on the half-line
Autorzy:
Mykytyuk, Yaroslav
Sushchyk, Natalia
Powiązania:
https://bibliotekanauki.pl/articles/1397872.pdf
Data publikacji:
2019
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
inverse scattering
Schroedinger operator
Banach algebra
Opis:
We describe the set of the scattering data for self-adjoint Sturm-Liouville operators on the half-line with potentials belonging to $L_1(\mathbb{R}_+, \rho(x) dx)$, where $ \rho : \mathbb{R}_+ \rightarrow \mathbb{R}_+$ is a monotonically nondecreasing function from some family $\mathcal{R}$. In particular, $\mathcal{R}$ includes the functions $\rho(x) = (1 +x)^\alpha$ with $ \alpha \geq 1$.
Źródło:
Opuscula Mathematica; 2019, 39, 4; 557-576
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On some fixed point theorems for expansive mappings in dislocated cone metric spaces with Banach algebras
Autorzy:
Auwalu, Abba
Hinçal, Evren
Mishra, Lakshmi Narayan
Powiązania:
https://bibliotekanauki.pl/articles/950882.pdf
Data publikacji:
2019
Wydawca:
Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
Tematy:
Banach algebra
expansive mapping
fixed point
algebra Banacha
mapowanie ekspensywne
punkt stały
sekwencja-c
Opis:
In this paper, we introduced the notion of generalized expansive mappings in dislocated cone metric spaces with Banach algebras. Furthermore, we prove some fixed point theorems for generalized expansive mappings in dislocated cone metric spaces with Banach algebras without the assumption of normality of cones. Moreover, we give an example to elucidate our result. Our results are significant extension and generalizations of many recent results in the literature.
Źródło:
Journal of Mathematics and Applications; 2019, 42; 21-33
1733-6775
2300-9926
Pojawia się w:
Journal of Mathematics and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Podręczniki do matematyki Stefana Banacha w kontekście doświadczeń szkolnych autora
Mathematics textbooks by Stefan Banach in the context of his school experiences
Autorzy:
Karpińska, Karolina
Powiązania:
https://bibliotekanauki.pl/articles/1398905.pdf
Data publikacji:
2019-06-30
Wydawca:
Polska Akademia Nauk. Instytut Historii Nauki im. Ludwika i Aleksandra Birkenmajerów
Tematy:
Stefan Banach
historia nauczania matematyki
historia matematyki
algebra
geometria
arytmetyka polityczna
matematyka finansowa
podręcznik szkolny
history of mathematics education
history of mathematics
geometry
political arithmetic
financial arithmetic
school textbook
Opis:
The aim of this paper is to analyse the content of school textbooks whose author or co-author was Stefan Banach (1892–1945), with particular attention paid to the scope of exploring equations, the method of introducing geometry to school teaching (whether to start it with discussing the basic planimetric concepts or basic stereometric concepts, or discussing them both parallelly?) and the range of political arithmetic (currently called financial arithmetic) problems. The paper examines the extent to which Banach’s textbooks were innovative in this respect. The research is based on, among others, the textbooks used by Banach as a secondary school student and the ordinances of the Polish ministry of education (Ministry of Religious Affairs and Public Education) from 1922.
Źródło:
Analecta. Studia i Materiały z Dziejów Nauki; 2019, 28, 1; 71-138
1509-0957
Pojawia się w:
Analecta. Studia i Materiały z Dziejów Nauki
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Inverse scattering problems for half-line Schrödinger operators and Banach algebras
Autorzy:
Mykytyuk, Y.
Sushchyk, N.
Powiązania:
https://bibliotekanauki.pl/articles/952791.pdf
Data publikacji:
2018
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
inverse scattering Schrodinger operator
Banach algebra
Opis:
The inverse scattering problem for half-line Schrodinger operators with potentials from the Marchenko class is shown to be closely related to some Banach algebra of functions on the line. In particular, it is proved that the topological conditions in the Marchenko theorem can be replaced by the condition that the scattering function should belong to this Banach algebra.
Źródło:
Opuscula Mathematica; 2018, 38, 5; 719-731
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Measures of noncompactness in a Banach algebra and their applications
Autorzy:
Dudek, S.
Powiązania:
https://bibliotekanauki.pl/articles/357842.pdf
Data publikacji:
2017
Wydawca:
Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
Tematy:
Banach algebra
integral equation of fractional order
fixed point theorem
asymptotic stability
ultimate monotonicity
measure of noncompactness
algebra Banacha
przestrzeń Banacha
równanie całkowite rzędu ułamkowego
twierdzenie o punkcie stałym
stabilność asymptotyczna
monotoniczność
Opis:
In this paper we study the existence of solutions of a nonlinear quadratic integral equation of fractional order. This equation is considered in the Banach space of real functions defined, continuous and bounded on the real half axis. Additionally, using the technique of measures of noncompactness we obtain some characterization of considered integral equation. We provide also an example illustrating the applicability of our approach.
Źródło:
Journal of Mathematics and Applications; 2017, 40; 69-84
1733-6775
2300-9926
Pojawia się w:
Journal of Mathematics and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Closed ideals in a new class of algebras of holomorphic functions on the disc
Autorzy:
Merino-Cruz, Hector
Wawrzyńczyk, Antoni
Powiązania:
https://bibliotekanauki.pl/articles/1912864.pdf
Data publikacji:
2014
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Banach algebra
disc algebra
standard ideal
Opis:
We define a new class of Banach algebras of holomorphic functions on the unit disc \(\mathbb{D}\) which contains the algebras studied in [GMR2] and [GW]. To a function G of the class \(\mathcal{A}^1 (\mathbb{D})\) nowhere vanishing in \(\mathbb{D}\) we associate a Banach algebra \(\mathcal{A}^n_G (\mathbb{D})\) contained in the disc algebra \(\mathcal{A}(\mathbb{D})\). We prove that all closed ideals of \(\mathcal{A}^n_G (\mathbb{D})\) of at most countable hull are of the standard form.
Źródło:
Commentationes Mathematicae; 2014, 54, 1
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Approximate homomorphisms and derivation in multi-Banach algebras
Autorzy:
Agarwal, Ravi P.
Cho, Yeol Je
Park, Choonkil
Saadati, Reza
Powiązania:
https://bibliotekanauki.pl/articles/1912850.pdf
Data publikacji:
2011
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Additive functional equation
fixed point
homomorphism in multi-Banach algebra
generalized Hyers-Ulam stability
derivation on multi-Banach algebra
multi-normed space
Opis:
Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in multi-Banach algebras and derivations on multi-Banach algebras for the additive functional equation \[ \sum_{i=1}^m f\left(mx_i+\sum_{j=1, j\not=i}^m x_j\right) + f\left(\sum_{i=1}^m x_i\right) = 2 f \left(\sum_{i=1}^{m} mx_i\right) \] for each \(m\in \mathbb{N}\) with \(m\geq 2\).
Źródło:
Commentationes Mathematicae; 2011, 51, 1
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Representation Theorem for \(\varphi\)-Bounded Variation of Functions in the Sense of Riesz
Autorzy:
Aziz, Wadie
Leiva, Hugo
Merentes, Nelson
Rzepka, Beata
Powiązania:
https://bibliotekanauki.pl/articles/746275.pdf
Data publikacji:
2010
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Bounded variation
function of bounded variation in the sense of Riesz
variations spaces
Banach space
algebra space
Opis:
In this paper we extend the well known Riesz lemma to the class of bounded \(\varphi\)-variation functions in the sense of Riesz defined on a rectangle \(I_a^b\subset \mathbb{R}^2\). This concept was introduced in [2], where the authors proved that the space \(BV_\varphi^R (I_a^b;\mathbb{R}\) of such functions is a Banach Algebra. Moreover, they characterized also the Nemytskii operator acting in this space. Thus our result creates a continuation of the paper [2].
Źródło:
Commentationes Mathematicae; 2010, 50, 2
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some remarks on the algebra of functions of two variables with bounded total \(\Phi\)-variation in Schramm sense
Autorzy:
Ereú, Tomás
Merentes, Nelson
Sánchez, José L.
Powiązania:
https://bibliotekanauki.pl/articles/745214.pdf
Data publikacji:
2010
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Bounded variation in the sense of Wiener
bounded total variation in the sense of Schramm
function of two variable
Banach algebra
Opis:
This paper is devoted to discuss some generalizations of the bounded total \(\Phi\)-variation in the sense of Schramm. This concept was defined by W. Schramm for functions of one real variable. In the paper we generalize the concept in question for the case of functions of of two variables defined on certain rectangle in the plane. The main result obtained in the paper asserts that the set of all functions having bounded total \(\Phi\)-variation in Schramm sense has the structure of a Banach algebra.
Źródło:
Commentationes Mathematicae; 2010, 50, 1
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An infinite dimensional Banach algebra with all but one maximal abelian subalgebras of dimension two
Autorzy:
Żelazko, Wiesław
Powiązania:
https://bibliotekanauki.pl/articles/960131.pdf
Data publikacji:
2008
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Abelian algebra
Bounded operators
Complex Banach space
Opis:
I construct a unital closed subalgebra of L(H) with the property announced in the title. Moreover, for any two maxiamal abelian subalgebras of the algebra in question, their intersection consists only of scalar multiples of the unity.
Źródło:
Commentationes Mathematicae; 2008, 48, 1
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Maximal abelian subalgebras of \(B(\mathcal{X})\)
Autorzy:
Bračič, Janko
Kuzma, Bojan
Powiązania:
https://bibliotekanauki.pl/articles/746718.pdf
Data publikacji:
2008
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Abelian algebra
Bounded operators
Complex Banach space
Opis:
Let \(\mathcal{X}\) be an infinite dimensional complex Banach space and \(B(\mathcal{X})\) be the Banach algebra of all bounded linear operators on \(\mathcal{X}\). Żelazko [1] posed the following question: Is it possible that some maximal abelian subalgebra of \(B(\mathcal{X})\) is finite dimensional? Interestingly, he was able to show that there does exist an infinite dimensional closed subalgebra of \(B(\mathcal{X})\) with all but one maximal abelian subalgebras of dimension two. The aim of this note is to give a negative answer to the original question and prove that there does not exist a finite dimensional maximal commutative subalgebra of \(B(\mathcal{X})\) if \(\text{dim} X = \infty\).
Źródło:
Commentationes Mathematicae; 2008, 48, 1
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Around Widders characterization of the Laplace transform of an element of $L^{∞}(ℝ^{+})$
Autorzy:
Kisyński, Jan
Powiązania:
https://bibliotekanauki.pl/articles/1207972.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
operators from $L_{ϰ}^{1}(ℝ^{+})$ into a Banach space
complete monotonicity and positivity with respect to a cone
one-parameter semigroups of operators
vector measures
Gelfand space
Radon-Nikodym property
representations of the convolution algebra $L_{ϰ}^{1}(ℝ^{+})$
pseudoresolvents and their generators
real inversion formulas for the Laplace transform
Opis:
Let ϰ be a positive, continuous, submultiplicative function on $ℝ^{+}$ such that $lim_{t→∞} e^{-ωt}t^{-α}ϰ(t) = a$ for some ω ∈ ℝ, α ∈ $\overline{ℝ^{+}}$ and $a ∈ ℝ^{+}$. For every λ ∈ (ω,∞) let $ϕ_{λ}(t) =e^{-λt}$ for $t ∈ ℝ^{+}$. Let $L^{1}_{ϰ}(ℝ^{+})$ be the space of functions Lebesgue integrable on $ℝ^{+}$ with weight $ϰ$, and let E be a Banach space. Consider the map $ϕ_{•}: (ω,∞) ∋ λ → ϕ_{λ} ∈ L_{ϰ}^{1}(ℝ^{+})$. Theorem 5.1 of the present paper characterizes the range of the linear map $T → Tϕ_{•}$ defined on $L(L_{ϰ}^{1}(ℝ^{+});E)$, generalizing a result established by B. Hennig and F. Neubrander for $ϰ(t)=e^{ωt}$. If ϰ ≡ 1 and E =ℝ then Theorem 5.1 reduces to D. V. Widder's characterization of the Laplace transform of a function in $L^{∞}(ℝ^{+})$. Some applications of Theorem 5.1 to the theory of one-parameter semigroups of operators are discussed. In particular a version of the Hille-Yosida generation theorem is deduced for $C_0$ semigroups $(S_t)_{t ∈ \overline{ℝ^{+}}}$ such that $sup_{t ∈ \overline{ℝ^{+}}} (ϰ(t))^{-1}∥ S_t∥ < ∞$.
Źródło:
Annales Polonici Mathematici; 2000, 74, 1; 161-200
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Commutative, radical amenable Banach algebras
Autorzy:
Read, C. J.
Powiązania:
https://bibliotekanauki.pl/articles/1206041.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
adical
Banach algebra
amenable
nilpotent
Opis:
There has been a considerable search for radical, amenable Banach algebras. Noncommutative examples were finally found by Volker Runde [R]; here we present the first commutative examples. Centrally placed within the construction, the reader may be pleased to notice a reprise of the undergraduate argument that shows that a normed space with totally bounded unit ball is finite-dimensional; we use the same idea (approximate the norm 1 vector x within distance η by a "good" vector $y_1$; then approximate $(x-y_1)/η$ within distance η by a "good" vector $y_2$, thus approximating x within distance $η^2$ by $y_1+η y_2$, and so on) to go from η=9/10 in Lemma 1.5 to arbitrarily small η in Lemma 2.1. This is not an arbitrary decision on the part of the author; it really is forced on him by the nature of the construction, see e.g. (6.1) for a place where η small at the start will not do.
Źródło:
Studia Mathematica; 2000, 140, 3; 199-212
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Cohens proof of the Factorization Theorem
Autorzy:
Kisyński, Jan
Powiązania:
https://bibliotekanauki.pl/articles/1207918.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
factorization for a representation of a Banach algebra with a bounded approximate identity
Opis:
Various proofs of the Factorization Theorem for representations of Banach algebras are compared with its original proof due to P. Cohen.
Źródło:
Annales Polonici Mathematici; 2000, 75, 2; 177-192
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 23

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