Geodesic
Borel equivalence relations in the space of bounded operators
Iian B. Smythe1
1 Department of Mathematics Cornell University Ithaca, NY 14853, U.S.A.
Fundamenta Mathematicae, Tome 237 (2017) no. 1, pp. 31-45

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm116-9-2016
Keywords: consider various notions equivalence space bounded operators hilbert space particular modulo finite rank modulo schatten p class modulo compact using hjorth theory turbulence latter shown classifiable countable structures while first reducible orbit equivalence relation polish group action results modulo finite rank modulo compact operators shown restrictions these equivalence relations space projection operators

Iian B. Smythe 1

1 Department of Mathematics Cornell University Ithaca, NY 14853, U.S.A. 
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Iian B. Smythe. Borel equivalence relations in the space of bounded operators. Fundamenta Mathematicae, Tome 237 (2017) no. 1, pp. 31-45. doi: 10.4064/fm116-9-2016

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