Relations between the Taylor spectrum and the Xia spectrum
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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 $\sigma _{X}(\mathbf { U},A)$.References
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Additional Information
- Muneo Chō
- Affiliation: Department of Mathematics, Kanagawa University, Yokohama 221-8686, Japan
- Email: m-cho@cc.kanagawa-u.ac.jp
- 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
- Communicated by: David R. Larson
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2357-2363
- MSC (1991): Primary 47B20
- DOI: https://doi.org/10.1090/S0002-9939-99-05335-6
- MathSciNet review: 1664357
Dedicated: Dedicated to Professor Jyunji Inoue on his sixtieth birthday