Temat: Banach Limits - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Quadratic inequalities for functionals in $l^{\infty}$
Autorzy:: Herzog, Gerd
Kunstmann, Peer Chr.
Powiązania:: https://bibliotekanauki.pl/articles/2051918.pdf
Data publikacji:: 2021
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: Banach algebras of bounded functions
operator-invariant functionals
Banach limits
Opis:: For a class of operators $T$ on $l^{\infty}$ and $T$-invariant functionals $\phi$ we prove inequalities between $\phi(x), \phi(x^{2})$ and the upper density of the sets \[P_{r} := \{n \in \mathbb{N}_{0} : \phi((T^{n}x)\cdot x) > r\}\] Applications are given to Banach limits and integrals.
Źródło:: Opuscula Mathematica; 2021, 41, 3; 437-446
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Generalized limits and a mean ergodic theorem
Autorzy:: Li, Yuan-Chuan
Shaw, Sen-Yen
Powiązania:: https://bibliotekanauki.pl/articles/1220908.pdf
Data publikacji:: 1996
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: Banach limits
$L$-limits
states
numerical radius
reflexive space
mean ergodic theorem
Opis:: For a given linear operator L on $ℓ^∞$ with ∥L∥ = 1 and L(1) = 1, a notion of limit, called the L-limit, is defined for bounded sequences in a normed linear space X. In the case where L is the left shift operator on $ℓ^∞$ and $X = ℓ^∞$, the definition of L-limit reduces to Lorentz's definition of σ-limit, which is described by means of Banach limits on $ℓ^∞$. We discuss some properties of L-limits, characterize reflexive spaces in terms of existence of L-limits of bounded sequences, and formulate a version of the abstract mean ergodic theorem in terms of L-limits. A theorem of Sinclair on the form of linear functionals on a unital normed algebra in terms of states is also generalized.
Źródło:: Studia Mathematica; 1996, 121, 3; 207-219
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Almost convergent sequence spaces derived by the domain of quadruple band matrix
Autorzy:: Bişgin, Mustafa Cemil
Powiązania:: https://bibliotekanauki.pl/articles/1794787.pdf
Data publikacji:: 2020-07-06
Wydawca:: Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
Tematy:: matrix domain
Schauder basis
beta- and gamma-duals
Banach Limits
almost convergence and matrix classes
Opis:: In this work, we construct the sequence spaces $f(Q(r,s,t,u))$, $f_0(Q(r,s,t,u))$ and $f_s(Q(r,s,t,u))$, where $Q(r,s,t,u)$ is quadruple band matrix which generalizes the matrices $Δ^{3}$, $B(r,s,t)$, $Δ^{2}$, $B(r,s)$ and $Δ$, where $Δ^{3}$, $B(r,s,t)$, $Δ^{2}$, $B(r,s)$ and $Δ$ are called third order difference, triple band, second order difference, double band and difference matrix, respectively. Also, we prove that these spaces are BK-spaces and are linearly isomorphic to the sequence spaces $f$, $f_0$ and $f_s$, respectively. Moreover, we give the Schauder basis and $β$-, $γ$-duals of those spaces. Lastly, we characterize some matrix classes related to those spaces.
Źródło:: Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica; 2020, 19; 155-170
2300-133X
Pojawia się w:: Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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