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

Saard Youyen, and Suthep Suantai. "On the H-property and rotundity of Cesàro direct sums of Banach spaces." Banach Center Publications 79.1 (2008): 247-252. <http://eudml.org/doc/281774>.

@article{SaardYouyen2008,
abstract = {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.},
author = {Saard Youyen, Suthep Suantai},
journal = {Banach Center Publications},
keywords = {direct sum of Banach spaces; -property; Schur property; Cesàro -norm; rotundity},
language = {eng},
number = {1},
pages = {247-252},
title = {On the H-property and rotundity of Cesàro direct sums of Banach spaces},
url = {http://eudml.org/doc/281774},
volume = {79},
year = {2008},
}

TY - JOUR
AU - Saard Youyen
AU - Suthep Suantai
TI - On the H-property and rotundity of Cesàro direct sums of Banach spaces
JO - Banach Center Publications
PY - 2008
VL - 79
IS - 1
SP - 247
EP - 252
AB - 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.
LA - eng
KW - direct sum of Banach spaces; -property; Schur property; Cesàro -norm; rotundity
UR - http://eudml.org/doc/281774
ER -