Subprojective Banach spaces

T. Oikhberg; E. Spinu

doi:10.1016/j.jmaa.2014.11.008

Subprojective Banach spaces

T. Oikhberg, E. Spinu

Mathematics

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

Abstract

A Banach space X is called subprojective if any of its infinite dimensional subspaces contains a further infinite dimensional subspace complemented in X. This paper is devoted to systematic study of subprojectivity. We examine the stability of subprojectivity of Banach spaces under various operations, such as direct or twisted sums, tensor products, and forming spaces of operators. Along the way, we obtain new classes of subprojective spaces.

Original language	English (US)
Pages (from-to)	613-635
Number of pages	23
Journal	Journal of Mathematical Analysis and Applications
Volume	424
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2014.11.008
State	Published - Apr 1 2015

Keywords

Banach space
Complemented subspace
Space of operators
Tensor product

ASJC Scopus subject areas

Analysis
Applied Mathematics

Online availability

10.1016/j.jmaa.2014.11.008

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title = "Subprojective Banach spaces",

abstract = "A Banach space X is called subprojective if any of its infinite dimensional subspaces contains a further infinite dimensional subspace complemented in X. This paper is devoted to systematic study of subprojectivity. We examine the stability of subprojectivity of Banach spaces under various operations, such as direct or twisted sums, tensor products, and forming spaces of operators. Along the way, we obtain new classes of subprojective spaces.",

keywords = "Banach space, Complemented subspace, Space of operators, Tensor product",

author = "T. Oikhberg and E. Spinu",

note = "Funding Information: The authors acknowledge the generous support of Simons Foundation , via its Travel Grant 210060 . They would also like to thank the organizers of Workshop in Linear Analysis at Texas A&M, where part of this work was carried out. Last but not least, they express their gratitude to L. Bunce, T. Schlumprecht, B. Sari, and N.-Ch. Wong for many helpful suggestions. Publisher Copyright: {\textcopyright} 2014 Elsevier Inc.",

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AU - Spinu, E.

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AB - A Banach space X is called subprojective if any of its infinite dimensional subspaces contains a further infinite dimensional subspace complemented in X. This paper is devoted to systematic study of subprojectivity. We examine the stability of subprojectivity of Banach spaces under various operations, such as direct or twisted sums, tensor products, and forming spaces of operators. Along the way, we obtain new classes of subprojective spaces.

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KW - Complemented subspace

KW - Space of operators

KW - Tensor product

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Subprojective Banach spaces

Abstract

Keywords

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