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 |
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Pages (from-to) | 91-114 |
Number of pages | 24 |
Journal | Integral Equations and Operator Theory |
Volume | 78 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jan 2014 |
Keywords
- Measurable operators
- non-commutative symmetric spaces
- p-convexity
- q-concavity