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

Banach Center Publications (2008)

- Volume: 79, Issue: 1, page 247-252
- ISSN: 0137-6934

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topSaard 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 -

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