Cesàro bounded operators in Banach spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00524149" target="_blank" >RIV/67985840:_____/20:00524149 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s11854-020-0085-8" target="_blank" >https://doi.org/10.1007/s11854-020-0085-8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11854-020-0085-8" target="_blank" >10.1007/s11854-020-0085-8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Cesàro bounded operators in Banach spaces

Popis výsledku v původním jazyce

We study several notions of boundedness for operators. It is known that any power bounded operator is absolutely Cesàro bounded and strongly Kreiss bounded (in particular, uniformly Kreiss bounded). The converses do not hold in general. In this note, we give examples of topologically mixing (hence, not power bounded) absolutely Cesàro bounded operators on ℓp(ℕ), 1 ≤ p < ∞, and provide examples of uniformly Kreiss bounded operators which are not absolutely Cesàro bounded. These results complement a few known examples (see [27] and [2]). We also obtain a characterization of power bounded operators which generalizes a result of Van Casteren [32]. In [2] Aleman and Suciu asked if every uniformly Kreiss bounded operator T on a Banach space satisfies that (Formula presented.). We solve this question for Hilbert space operators and, moreover, we prove that, if T is absolutely Cesàro bounded on a Banach (Hilbert) space, then ∥Tn∥ = o(n) ((∥Tn∥=o(n12), respectively). As a consequence, every absolutely Cesàro bounded operator on a reflexive Banach space is mean ergodic.

Název v anglickém jazyce

Cesàro bounded operators in Banach spaces

Popis výsledku anglicky

We study several notions of boundedness for operators. It is known that any power bounded operator is absolutely Cesàro bounded and strongly Kreiss bounded (in particular, uniformly Kreiss bounded). The converses do not hold in general. In this note, we give examples of topologically mixing (hence, not power bounded) absolutely Cesàro bounded operators on ℓp(ℕ), 1 ≤ p < ∞, and provide examples of uniformly Kreiss bounded operators which are not absolutely Cesàro bounded. These results complement a few known examples (see [27] and [2]). We also obtain a characterization of power bounded operators which generalizes a result of Van Casteren [32]. In [2] Aleman and Suciu asked if every uniformly Kreiss bounded operator T on a Banach space satisfies that (Formula presented.). We solve this question for Hilbert space operators and, moreover, we prove that, if T is absolutely Cesàro bounded on a Banach (Hilbert) space, then ∥Tn∥ = o(n) ((∥Tn∥=o(n12), respectively). As a consequence, every absolutely Cesàro bounded operator on a reflexive Banach space is mean ergodic.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA17-27844S" target="_blank" >GA17-27844S: Generické objekty</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal D Analyse Mathematique

ISSN

0021-7670

e-ISSN

—

Svazek periodika

140

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

IL - Stát Izrael

Počet stran výsledku

20

Strana od-do

187-206

Kód UT WoS článku

000525081600002

EID výsledku v databázi Scopus

2-s2.0-85083798906