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

Saard  Youyen; Suthep Suantai

Banach Center Publications, Tome 83 (2008), p. 247-252 / Harvested from The Polish Digital Mathematics Library

Résumé

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

Publié le : 2008-01-01

Zbl 1173.46007

EUDML-ID : urn:eudml:doc:281774

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc79-0-20,
     author = {Saard  Youyen and Suthep Suantai},
     title = {On the H-property and rotundity of Ces\`aro direct sums of Banach spaces},
     journal = {Banach Center Publications},
     volume = {83},
     year = {2008},
     pages = {247-252},
     zbl = {1173.46007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc79-0-20}
}

Saard  Youyen; Suthep Suantai. On the H-property and rotundity of Cesàro direct sums of Banach spaces. Banach Center Publications, Tome 83 (2008) pp. 247-252. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc79-0-20/