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Hokkaido University Preprint Series in Mathematics >
Weyl-von Neumann Theorem and Borel Complexity of Unitary Equivalence Modulo Compacts of Self-Adjoint Operators
| Title: | Weyl-von Neumann Theorem and Borel Complexity of Unitary Equivalence Modulo Compacts of Self-Adjoint Operators |
| Authors: | Ando, Hiroshi Browse this author | | Matsuzawa, Yasumichi Browse this author |
| Keywords: | Weyl-von Neumann Theorem | | Self-adjoint operators | | Turbulence. |
| Issue Date: | 30-Apr-2014 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1053 |
| Start Page: | 1 |
| End Page: | 20 |
| Abstract: | 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. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69857 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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