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Displaying similar documents to “Compact diagonal linear operators on Banach spaces with unconditional bases.”

On strong M-bases in Banach spaces with PRI.

Deba P. Sinha (2000)

Collectanea Mathematica

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If every member of a class P of Banach spaces has a projectional resolution of the identity such that certain subspaces arising out of this resolution are also in the class P, then it is proved that every Banach space in P has a strong M-basis. Consequently, every weakly countably determined space, the dual of every Asplund space, every Banach space with an M-basis such that the dual unit ball is weak* angelic and every C(K) space for a Valdivia compact set K , has a strong M-basis. ...

Uniformly Gâteaux Differentiable Norms in Spaces with Unconditional Basis

Rychter, Jan (2000)

Serdica Mathematical Journal

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*Supported in part by GAˇ CR 201-98-1449 and AV 101 9003. This paper is based on a part of the author’s MSc thesis written under the supervison of Professor V. Zizler. It is shown that a Banach space X admits an equivalent uniformly Gateaux differentiable norm if it has an unconditional basis and X* admits an equivalent norm which is uniformly rotund in every direction.