Relations between the Taylor spectrum and the Xia spectrum

Chō, Muneo

doi:10.1090/S0002-9939-99-05335-6

Relations between the Taylor spectrum and the Xia spectrum
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by Muneo Chō PDF

Proc. Amer. Math. Soc. 128 (2000), 2357-2363 Request permission

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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