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On the H-property and rotundity of Cesàro direct sums of Banach spaces

Tom 79 / 2008

Saard Youyen, Suthep Suantai Banach Center Publications 79 (2008), 247-252 MSC: 47H10, 47H09. DOI: 10.4064/bc79-0-20

Streszczenie

In this paper, we define the direct sum $(\oplus^{n}_{i=1}X_i)_{{\rm ces}_p}$ of Banach spaces $X_1,X_2,\dots,$ and $X_n$ and consider it equipped with the Cesàro $p$-norm when $1\leq p< \infty$. We show that $(\oplus^{n}_{i=1}X_i)_{{\rm ces}_p}$ has the H-property if and only if each $X_i$ has the H-property, and $(\oplus^{n}_{i=1}X_i)_{{\rm ces}_p}$ has the Schur property if and only if each $X_i$ has the Schur property. Moreover, we also show that $(\oplus^{n}_{i=1}X_i)_{{\rm ces}_p}$ is rotund if and only if each $X_i$ is rotund.

Autorzy

  • Saard YouyenDepartment of Mathematics
    Faculty of Science
    Naresuan University
    Pitsanuloke, 55000, Thailand
    e-mail
  • Suthep SuantaiDepartment of Mathematics
    Faculty of Science
    Chiang Mai University
    Chiang Mai, 50200, Thailand
    e-mail

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