A note on the column-row property
Samya Kumar Ray, Srijan Sarkar
TL;DR
This paper classifies which non-commutative Lp spaces over semifinite von Neumann algebras satisfy the column-row property, exploring related properties and their presence in natural operator space examples.
Contribution
It provides a complete classification of the column-row property for non-commutative Lp spaces over semifinite von Neumann algebras.
Findings
Classification of the column-row property for non-commutative Lp spaces
Analysis of related operator space properties
Discussion of property existence in natural examples
Abstract
In this article, we study the following question asked by Michael Hartz in a recent paper \cite{Hartz}: \textit{which operator spaces satisfy the column-row property?} We provide a complete classification of the column-row property for non-commutative -spaces over semifinite von Neumann algebras. We study other relevant properties of operator spaces that are related to the column-row property and discuss their existence and non-existence for various natural examples of operator spaces.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Banach Space Theory · Mathematical Analysis and Transform Methods