Borel equivalence relations in the space of bounded operators

DOI10.4064/FM116-9-2016zbMATH Open1420.03124arXiv1407.5325OpenAlexW2963281599MaRDI QIDQ2966799

Iian B. Smythe

Publication date: 8 March 2017

Published in: Fundamenta Mathematicae (Search for Journal in Brave)

Abstract: We consider various notions of equivalence in the space of bounded operators on a Hilbert space, in particular modulo finite rank, modulo Schatten $p$-class, and modulo compact. Using Hjorth's theory of turbulence, the latter two are shown to be not classifiable by countable structures, while the first is not reducible to the orbit equivalence relation of any Polish group action. The results for modulo finite rank and modulo compact operators are also shown for the restrictions of these equivalence relations to the space of projection operators.

Full work available at URL: https://arxiv.org/abs/1407.5325

zbMATH Keywords

projection operatorsturbulenceBorel equivalence relationscompact operatorsCalkin algebraSchatten \(p\)-class

Mathematics Subject Classification ID

Descriptive set theory (03E15) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10)

Related Items (1)

On Borel equivalence relations in generalized Baire space

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