On p-Convexity and q-Concavity in Non-Commutative Symmetric Spaces

Peter Dodds; Theresa Dodds; Fyodor Sukochev

doi:10.1007/s00020-013-2082-0

On p-Convexity and q-Concavity in Non-Commutative Symmetric Spaces

Peter Dodds, Theresa Dodds, Fyodor Sukochev

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

24 Citations (Scopus)

Abstract

It is shown that if a symmetric Banach space E on the positive semi-axis is p-convex (q-concave) then so is the corresponding non-commutative symmetric space E(τ) of τ-measurable operators affiliated with some semifinite von Neumann algebra (M, τ), with preservation of the convexity (concavity) constants in the case that M is non-atomic. Similar statements hold in the case that E satisfies an upper (lower) p-estimate and extend to the more general semifinite setting earlier results due to Arazy and Lin for unitary matrix spaces.

Original language	English
Pages (from-to)	91-114
Number of pages	24
Journal	Integral Equations and Operator Theory
Volume	78
Issue number	1
DOIs	https://doi.org/10.1007/s00020-013-2082-0
Publication status	Published - Jan 2014

Keywords

Measurable operators
non-commutative symmetric spaces
p-convexity
q-concavity

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AB - It is shown that if a symmetric Banach space E on the positive semi-axis is p-convex (q-concave) then so is the corresponding non-commutative symmetric space E(τ) of τ-measurable operators affiliated with some semifinite von Neumann algebra (M, τ), with preservation of the convexity (concavity) constants in the case that M is non-atomic. Similar statements hold in the case that E satisfies an upper (lower) p-estimate and extend to the more general semifinite setting earlier results due to Arazy and Lin for unitary matrix spaces.

KW - Measurable operators

KW - non-commutative symmetric spaces

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KW - q-concavity

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JF - Integral Equations and Operator Theory

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On p-Convexity and q-Concavity in Non-Commutative Symmetric Spaces

Abstract

Keywords

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