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

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Youyen S., Suantai S.

Banach Center Publications

2008

tom 79

nr 1

247-252

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.

Ograniczanie wyników

1 Banach Center Publications

1 Suantai S.

1 Youyen S.

1 2008

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