Weyl-von Neumann Theorem and Borel Complexity of Unitary Equivalence Modulo Compacts of Self-Adjoint Operators

Ando, Hiroshi; Matsuzawa, Yasumichi

Hokkaido University Preprint Series in Mathematics, 2014, 1053, 1-20

Permalink : https://doi.org/10.14943/84197

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アクセス権	open access
DOI	https://doi.org/10.14943/84197
URI	https://hdl.handle.net/2115/69857
タイトル	Weyl-von Neumann Theorem and Borel Complexity of Unitary Equivalence Modulo Compacts of Self-Adjoint Operators
著者	著者名 Ando, Hiroshi
著者	著者名 Matsuzawa, Yasumichi
言語	英語
キーワード	Weyl-von Neumann Theorem
	Self-adjoint operators
	Turbulence.
発行日	2014-04-30
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	1053
ページ	1-20
抄録	Weyl-von Neumann Theorem asserts that two bounded self-adjoint operators A;B on a Hilbert space H are unitarily equivalent modulo compacts, i.e., uAu +K = B for some unitary u 2 U(H) and compact self-adjoint operator K, if and only if A and B have the same essential spectra: ess(A) = ess(B). In this paper we consider to what extent the above Weyl-von Neumann's result can(not) be extended to unbounded operators using descriptive set theory. We show that if H is separable in nite-dimensional, this equivalence relation for bounded self-adjoin operators is smooth, while the same equivalence relation for general self-adjoint operators contains a dense G -orbit but does not admit classi cation by countable structures. On the other hand, apparently related equivalence relation A B , 9u 2 U(H) [u(A 􀀀 i) 􀀀1u 􀀀 (B 􀀀 i) 􀀀1 is compact], is shown to be smooth.
資源タイプ	紀要論文
出版タイプ	Version of Record