Cesàro bounded operators in Banach spaces
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Cesàro bounded operators in Banach spaces
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA17-27844S" target="_blank" >GA17-27844S: Generic objects</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal D Analyse Mathematique
ISSN
0021-7670
e-ISSN
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Volume of the periodical
140
Issue of the periodical within the volume
1
Country of publishing house
IL - THE STATE OF ISRAEL
Number of pages
20
Pages from-to
187-206
UT code for WoS article
000525081600002
EID of the result in the Scopus database
2-s2.0-85083798906