Weyl-von Neumann Theorem and Borel Complexity of Unitary Equivalence Modulo Compacts of Self-Adjoint Operators
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.
収録刊行物
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- Hokkaido University Preprint Series in Mathematics
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Hokkaido University Preprint Series in Mathematics 1053 1-20, 2014-04-30
Department of Mathematics, Hokkaido University
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詳細情報 詳細情報について
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- CRID
- 1390290699772187648
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- NII論文ID
- 120006459742
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- DOI
- 10.14943/84197
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- HANDLE
- 2115/69857
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- 本文言語コード
- en
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- データソース種別
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- JaLC
- IRDB
- CiNii Articles
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- 抄録ライセンスフラグ
- 使用可