Genericity of Certain Classes of Unitary and Self-Adjoint Operators
Canadian mathematical bulletin, Tome 41 (1998) no. 2, pp. 137-139
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In a paper [1], published in 1990, in a (somewhat inaccessible) conference proceedings, the authors had shown that for the unitary operators on a separable Hilbert space, endowed with the strong operator topology, those with singular, continuous, simple spectrum, with full support, forma dense ${{G}_{\delta }}$ . A similar theorem for bounded self-adjoint operators with a given normbound (omitting simplicity) was recently given by Barry Simon [2], [3], with a totally different proof. In this note we show that a slight modification of our argument, combined with the Cayley transform, gives a proof of Simon’s result, with simplicity of the spectrum added.
Choksi, J. R.; Nadkarni, M. G. Genericity of Certain Classes of Unitary and Self-Adjoint Operators. Canadian mathematical bulletin, Tome 41 (1998) no. 2, pp. 137-139. doi: 10.4153/CMB-1998-021-4
@article{10_4153_CMB_1998_021_4,
author = {Choksi, J. R. and Nadkarni, M. G.},
title = {Genericity of {Certain} {Classes} of {Unitary} and {Self-Adjoint} {Operators}},
journal = {Canadian mathematical bulletin},
pages = {137--139},
year = {1998},
volume = {41},
number = {2},
doi = {10.4153/CMB-1998-021-4},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-021-4/}
}
TY - JOUR AU - Choksi, J. R. AU - Nadkarni, M. G. TI - Genericity of Certain Classes of Unitary and Self-Adjoint Operators JO - Canadian mathematical bulletin PY - 1998 SP - 137 EP - 139 VL - 41 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-021-4/ DO - 10.4153/CMB-1998-021-4 ID - 10_4153_CMB_1998_021_4 ER -
%0 Journal Article %A Choksi, J. R. %A Nadkarni, M. G. %T Genericity of Certain Classes of Unitary and Self-Adjoint Operators %J Canadian mathematical bulletin %D 1998 %P 137-139 %V 41 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-021-4/ %R 10.4153/CMB-1998-021-4 %F 10_4153_CMB_1998_021_4
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