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

• Autorzy: Saard Youyen , Suthep Suantai
• Języki publikacji: EN

Abstrakty

EN

In this paper, we define the direct sum $(⨁ ^{n}_{i=1} X_i)_{ces_p}$ of Banach spaces X₁,X₂,..., and Xₙ and consider it equipped with the Cesàro p-norm when 1 ≤ p < ∞. We show that $(⨁ ^{n}_{i=1}X_i)_{ces_p}$ has the H-property if and only if each $X_i$ has the H-property, and $(⨁ ^{n}_{i=1}X_i)_{ces_p}$ has the Schur property if and only if each $X_i$ has the Schur property. Moreover, we also show that $(⨁ ^{n}_{i=1}X_i)_{ces_p}$ is rotund if and only if each $X_i$ is rotund.

Kategorie tematyczne

• 47H09: Contraction-type mappings, nonexpansive mappings, A -proper mappings, etc.
• 47H10: Fixed-point theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2008
• Tom: 79
• Numer: 1
• Strony: 247-252

Daty

wydano

2008

Twórcy

autor

Saard Youyen

• Department of Mathematics, Faculty of Science, Naresuan University, Pitsanuloke, 55000, Thailand

autor

Suthep Suantai

• Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand

Identyfikatory

DOI

10.4064/bc79-0-20