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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Relations between the Taylor spectrum
and the Xia spectrum


Author: Muneo Cho
Journal: Proc. Amer. Math. Soc. 128 (2000), 2357-2363
MSC (1991): Primary 47B20
Published electronically: December 7, 1999
MathSciNet review: 1664357
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Abstract: Let $\mathbf{ T} = (T_{1},T_{2},...,T_{n})$ be a doubly commuting $n$-tuple of $p$-hyponormal operators $T_{j}$ with unitary operators $U_{j}$ from the polar decompositions $T_{j} = U_{j}|T_{j}| \ (j=1,...,n)$. Let $\mathbf{ U} = (U_{1},...,U_{n})$ and $A = |T_{1}| \cdots |T_{n}|$. In this paper, we will show relations between the Taylor spectrum $\sigma _{T}(\mathbf{ T})$ and the Xia spectrum $\sigma _{X}(\mathbf{ U},A)$.


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Additional Information

Muneo Cho
Affiliation: Department of Mathematics, Kanagawa University, Yokohama 221-8686, Japan
Email: m-cho@cc.kanagawa-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05335-6
PII: S 0002-9939(99)05335-6
Keywords: Putnam's inequality, Taylor spectrum, Xia spectrum, generalized polar symbols
Received by editor(s): March 12, 1998
Received by editor(s) in revised form: September 18, 1998
Published electronically: December 7, 1999
Additional Notes: This research was partially supported by Grant-in-Aid Scientific Research No.09640229
Dedicated: Dedicated to Professor Jyunji Inoue on his sixtieth birthday
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society