On the H-property and rotundity of Cesàro direct sums of Banach spaces
Volume 79 / 2008
Banach Center Publications 79 (2008), 247-252
MSC: 47H10, 47H09.
DOI: 10.4064/bc79-0-20
Abstract
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.
