Injectivity and projectivity in p-multinormed spaces

T. Oikhberg

doi:10.1007/s11117-018-0557-6

Injectivity and projectivity in p-multinormed spaces

T. Oikhberg

Mathematics

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

Abstract

We find large classes of injective and projective p-multinormed spaces. In fact, these classes are universal, in the sense that every p-multinormed space embeds into (is a quotient of) an injective (resp. projective) p-multinormed space. As a consequence, we show that any p-multinormed space has a canonical representation as a subspace of a quotient of a Banach lattice.

Original language	English (US)
Pages (from-to)	1023-1037
Number of pages	15
Journal	Positivity
Volume	22
Issue number	4
DOIs	https://doi.org/10.1007/s11117-018-0557-6
State	Published - Sep 1 2018

Keywords

Banach lattice
Injective object
Multinormed space
Projective object

ASJC Scopus subject areas

Analysis
Theoretical Computer Science
General Mathematics

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10.1007/s11117-018-0557-6

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title = "Injectivity and projectivity in p-multinormed spaces",

abstract = "We find large classes of injective and projective p-multinormed spaces. In fact, these classes are universal, in the sense that every p-multinormed space embeds into (is a quotient of) an injective (resp. projective) p-multinormed space. As a consequence, we show that any p-multinormed space has a canonical representation as a subspace of a quotient of a Banach lattice.",

keywords = "Banach lattice, Injective object, Multinormed space, Projective object",

author = "T. Oikhberg",

note = "Acknowledgements This work was partially supported by the Simons Foundation Travel Award 210060. The author wishes to thank his co-authors on [3] (G. Dales, N. Laustsen, and V. Troitsky), as well as A. Helemskii and N. Nemesh, for many stimulating conversations. The author is grateful to the anonymous referee for many helpful comments.",

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N1 - Acknowledgements This work was partially supported by the Simons Foundation Travel Award 210060. The author wishes to thank his co-authors on [3] (G. Dales, N. Laustsen, and V. Troitsky), as well as A. Helemskii and N. Nemesh, for many stimulating conversations. The author is grateful to the anonymous referee for many helpful comments.

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Y1 - 2018/9/1

N2 - We find large classes of injective and projective p-multinormed spaces. In fact, these classes are universal, in the sense that every p-multinormed space embeds into (is a quotient of) an injective (resp. projective) p-multinormed space. As a consequence, we show that any p-multinormed space has a canonical representation as a subspace of a quotient of a Banach lattice.

AB - We find large classes of injective and projective p-multinormed spaces. In fact, these classes are universal, in the sense that every p-multinormed space embeds into (is a quotient of) an injective (resp. projective) p-multinormed space. As a consequence, we show that any p-multinormed space has a canonical representation as a subspace of a quotient of a Banach lattice.

KW - Banach lattice

KW - Injective object

KW - Multinormed space

KW - Projective object

UR - https://www.scopus.com/pages/publications/85040941439

UR - https://www.scopus.com/pages/publications/85040941439#tab=citedBy

U2 - 10.1007/s11117-018-0557-6

DO - 10.1007/s11117-018-0557-6

M3 - Article

AN - SCOPUS:85040941439

SN - 1385-1292

VL - 22

SP - 1023

EP - 1037

JO - Positivity

JF - Positivity

IS - 4

ER -

Injectivity and projectivity in p-multinormed spaces

Abstract

Keywords

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