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Relations between the Taylor spectrum and the Xia spectrum

Authors:	Muneo Cho

Institution:	Department of Mathematics, Kanagawa University, Yokohama 221-8686, Japan

Abstract:	Let $\mathbf{ T} = (T_{1},T_{2},...,T_{n})$ be a doubly commuting -tuple of -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 $\sigma _{X}(\mathbf{ U},A)$ .

Keywords:	Putnam's inequality Taylor spectrum Xia spectrum generalized polar symbols

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