Unital operator spaces and discrete groups
Nikolaos Koutsonikos-Kouloumpis

TL;DR
This paper studies unital operator spaces with the trivial intersection property, showing they lack nontrivial boundary ideals, and explores their structure, isometries, and connections to group properties.
Contribution
It introduces the trivial intersection property for operator spaces, characterizes spaces with this property, and links these spaces to algebraic properties of groups.
Findings
Spaces with the trivial intersection property have no nontrivial boundary ideals.
Unital operator spaces on ()) containing ()) possess the trivial intersection property.
Complete isometries between such spaces are unitary equivalences.
Abstract
We introduce the trivial intersection property for concrete operator spaces and we show that a unital space with this property has no nontrivial boundary ideals. We provide various examples of such spaces, among which are strongly reflexive masa bimodules and completely distributive CSL algebras. We show that unital operator spaces acting on for any set , that contain the masa , possess the trivial intersection property, and we use this to prove that a unital surjective complete isometry between such spaces is a unitary equivalence. Then, we apply these results to -closed -bimodules acting on for a group and we relate them to algebraic properties of .
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Taxonomy
Topicsadvanced mathematical theories · Mathematical Analysis and Transform Methods · Spectral Theory in Mathematical Physics
