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On the Weyl Spectrum: Spectral Mapping Theorem and Weyl's Theorem

✍ Scribed by Jin-Chuan Hou; Xiu-Ling Zhang

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 153 KB
Volume: 220
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5897

No coin nor oath required. For personal study only.

✦ Synopsis

respectively for the spectrum and the Weyl spectrum of T ; moreover, Weyl's Ž . theorem holds for f T q F if ''dominant'' is replaced by ''M-hyponormal,'' where F is any finite rank operator commuting with T. These generalize earlier results for hyponormal operators. It is also shown that there exist an operator T and a finite rank operator F commuting with T such that Weyl's theorem holds for T but not Ž for T q F. This answers negatively a problem raised by K. K. Oberai Illinois J.

. Math. 21, 1977, 84᎐90 . However, if T is required to be isoloid, then the statement that Weyl's theorem holds for T will imply it holds for T q F.

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