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Wyświetlanie 1-10 z 45
Tytuł:
Algebraic polynomially bounded operators
Autorzy:
Mlak, W.
Powiązania:
https://bibliotekanauki.pl/articles/716527.pdf
Data publikacji:
1974
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Źródło:
Annales Polonici Mathematici; 1974-1975, 29, 2; 133-139
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the mean ergodic theorem for Cesàro bounded operators
Autorzy:
Derriennic, Yves
Powiązania:
https://bibliotekanauki.pl/articles/965638.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:
For a Cesàro bounded operator in a Hilbert space or a reflexive Banach space the mean ergodic theorem does not hold in general. We give an additional geometrical assumption which is sufficient to imply the validity of that theorem. Our result yields the mean ergodic theorem for positive Cesàro bounded operators in $L^{p}$ (1 < p < ∞). We do not use the tauberian theorem of Hardy and Littlewood, which was the main tool of previous authors. Some new examples, interesting for summability theory, are described: we build an example of a mean ergodic operator T in a Hilbert space such that $∥T^{n}∥/n$ does not converge to 0, and whose adjoint operator is not mean ergodic (its Cesàro averages converge only weakly).
Źródło:
Colloquium Mathematicum; 2000, 84/85, 2; 443-455
0010-1354
Pojawia się w:
Colloquium Mathematicum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the growth of the resolvent operators for power bounded operators
Autorzy:
Nevanlinna, Olavi
Powiązania:
https://bibliotekanauki.pl/articles/1358683.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:
Outline. In this paper I discuss some quantitative aspects related to power bounded operators T and to the decay of $T^{n}(T-1)$. For background I refer to two recent surveys J. Zemánek [1994], C. J. K. Batty [1994]. Here I try to complement these two surveys in two different directions. First, if the decay of $T^{n}(T-1)$ is as fast as O(1/n) then quite strong conclusions can be made. The situation can be thought of as a discrete version of analytic semigroups; I try to motivate this in Section 1 by demonstrating the similarity and lack of it between power boundedness of T and uniform boundedness of $e^{t(cT-1)}$ where c is a constant of modulus 1 and t > 0. Section 2 then contains the main result in this direction. I became interested in studying the quantitative aspects of the decay of $T^{n}(T-1)$ since it can be used as a simple model for what happens in the early phase of an iterative method (O. Nevanlinna [1993]). Secondly, the so called Kreiss matrix theorem relates bounds for the powers to bounds for the resolvent. The estimate is proportional to the dimension of the space and thus has as such no generalization to operators. However, qualitatively such a result holds in Banach spaces e.g. for Riesz operators: if the resolvent satisfies the resolvent condition, then the operator is power bounded operator (but without an estimate). I introduce in Section 3 a growth function for bounded operators. This allows one to obtain a result of the form: if the resolvent condition holds and if the growth function is finite at 1, then the powers are bounded and can be estimated. In Section 4 in addition to the Kreiss matrix theorem, two other applications of the growth function are given.
Źródło:
Banach Center Publications; 1997, 38, 1; 247-264
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Unbounded well-bounded operators, strongly continuous semigroups and the Laplace transform
Autorzy:
deLaubenfels, Ralph
Powiązania:
https://bibliotekanauki.pl/articles/1293082.pdf
Data publikacji:
1992
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:
Suppose A is a (possibly unbounded) linear operator on a Banach space. We show that the following are equivalent. (1) A is well-bounded on [0,∞). (2) -A generates a strongly continuous semigroup ${e^{-sA}}_{s≤0}$ such that ${(1/s^2)e^{-sA}}_{s>0}$ is the Laplace transform of a Lipschitz continuous family of operators that vanishes at 0. (3) -A generates a strongly continuous differentiable semigroup ${e^{-sA}}_{s≥0}$ and ∃ M < ∞ such that $∥H_n(s)∥ ≡ ∥(∑_{k=0}^n (s^k A^{k})/k!) e^{-sA}∥ ≤ M$, ∀s > 0, n ∈ ℕ ∪ {0}. (4) -A generates a strongly continuous holomorphic semigroup ${e^{-zA}}_{Re(z)>0}$ that is O(|z|) in all half-planes Re(z) > a > 0 and $K(t) ≡ ʃ_{1+iℝ} e^{zt} e^{-zA} dz/(2πiz^3)$ defines a differentiable function of t, with Lipschitz continuous derivative, with K'(0) = 0. We may then construct a decomposition of the identity, F, for A, from K(t) or $H_n(s)$. For ϕ ∈ X*, x ∈ X, $(F(t)ϕ)(x) = (d/dt)^2 (ϕ(K(t)x)) = lim_{n→∞} ϕ(H_n(n/t)x)$, for almost all t.
Źródło:
Studia Mathematica; 1992, 103, 2; 143-159
0039-3223
Pojawia się w:
Studia Mathematica
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:
Multipliers of Hardy spaces, quadratic integrals and Foiaş-Williams-Peller operators
Autorzy:
Blower, G.
Powiązania:
https://bibliotekanauki.pl/articles/1217911.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
polynomially bounded operators
Hankel operators
multipliers
Carleson measures
Opis:
We obtain a sufficient condition on a B(H)-valued function φ for the operator $⨍ ↦ Γ_φ ⨍'(S)$ to be completely bounded on $H^∞ B(H)$; the Foiaş-Williams-Peller operator | S^t Γ_φ | R_φ = | | | 0 S | is then similar to a contraction. We show that if ⨍ : D → B(H) is a bounded analytic function for which $(1-r) ||⨍'(re^{iθ})||^2_{B(H)} rdrdθ$ and $(1-r) ||⨍"(re^{iθ})||_{B(H)} rdrdθ$ are Carleson measures, then ⨍ multiplies $(H^1c^1)'$ to itself. Such ⨍ form an algebra A, and when φ'∈ BMO(B(H)), the map $⨍ ↦ Γ_φ ⨍'(S)$ is bounded $A → B(H^2(H), L^2(H) ⊖ H^2(H))$. Thus we construct a functional calculus for operators of Foiaş-Williams-Peller type.
Źródło:
Studia Mathematica; 1998, 131, 2; 179-188
0039-3223
Pojawia się w:
Studia Mathematica
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:
On invariant measures for power bounded positive operators
Autorzy:
Sato, Ryotaro
Powiązania:
https://bibliotekanauki.pl/articles/1287342.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
power bounded and Cesàro bounded positive operators
invariant measures
$L_1$ spaces
Opis:
We give a counterexample showing that $\overline{(I-T*)L_{∞}} ∩ L^{+}_{∞} = {0}$ does not imply the existence of a strictly positive function u in $L_1$ with Tu = u, where T is a power bounded positive linear operator on $L_1$ of a σ-finite measure space. This settles a conjecture by Brunel, Horowitz, and Lin.
Źródło:
Studia Mathematica; 1996, 120, 2; 183-189
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-10 z 45

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