Banach spaces which admit a norm with the uniform Kadec-Klee property

• Autorzy: S. J. Dilworth , Maria Girardi , Denka Kutzarova
• Języki publikacji: EN

Abstrakty

EN

Several results are established about Banach spaces Ӿ which can be renormed to have the uniform Kadec-Klee property. It is proved that all such spaces have the complete continuity property. We show that the renorming property can be lifted from Ӿ to the Lebesgue-Bochner space $L_2(Ӿ)$ if and only if Ӿ is super-reflexive. A basis characterization of the renorming property for dual Banach spaces is given.

Kategorie tematyczne

• 46B22: Radon-Nikod{\'y}m, Kre{\u\i}n-Milman and related properties
• 46B20: Geometry and structure of normed linear spaces
• 46G99: None of the above, but in this section
• 46B28: Spaces of operators; tensor products; approximation properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994-1995
• Tom: 112
• Numer: 3
• Strony: 267-277

Daty

wydano

1995

otrzymano

1993-10-21

poprawiono

1994-05-12

Twórcy

autor

S. J. Dilworth

• Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208, U.S.A.

autor

Maria Girardi

• Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208, U.S.A.

autor

Denka Kutzarova

• Institute of Mathematics, Bulgarian Academy of Sciences, 1090 Sofia, Bulgaria.

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