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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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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

  • 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