Norming subspaces of banach spaces

V. P. Fonf; S. Lajara; S. Troyanski; C. Zanco

doi:10.1090/proc/14442

Norming subspaces of banach spaces

V. P. Fonf, S. Lajara, S. Troyanski, C. Zanco

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that if X is a closed subspace of a Banach space E and Z is a closed subspace of E* such that Z is norming for X and X is total over Z (as well as X is norming for Z and Z is total over X), then X and the preannihilator of Z are complemented in E whenever Z is w*-closed or X is reflexive.

Original language	English
Pages (from-to)	3039-3045
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	147
Issue number	7
DOIs	https://doi.org/10.1090/proc/14442
State	Published - 1 Jan 2019

Keywords

M-bibasic system
Norming subspace
Reflexive subspace
Total subspace

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/proc/14442

Cite this

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abstract = "We show that if X is a closed subspace of a Banach space E and Z is a closed subspace of E* such that Z is norming for X and X is total over Z (as well as X is norming for Z and Z is total over X), then X and the preannihilator of Z are complemented in E whenever Z is w*-closed or X is reflexive.",

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AU - Troyanski, S.

AU - Zanco, C.

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N2 - We show that if X is a closed subspace of a Banach space E and Z is a closed subspace of E* such that Z is norming for X and X is total over Z (as well as X is norming for Z and Z is total over X), then X and the preannihilator of Z are complemented in E whenever Z is w*-closed or X is reflexive.

AB - We show that if X is a closed subspace of a Banach space E and Z is a closed subspace of E* such that Z is norming for X and X is total over Z (as well as X is norming for Z and Z is total over X), then X and the preannihilator of Z are complemented in E whenever Z is w*-closed or X is reflexive.

KW - M-bibasic system

KW - Norming subspace

KW - Reflexive subspace

KW - Total subspace

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Norming subspaces of banach spaces

Abstract

Keywords

ASJC Scopus subject areas

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