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2014 Tensor products and the spectral continuity for $k$-quasi-$\ast$-class A operators
Fugen Gao, Xiaochun Li
Banach J. Math. Anal. 8(1): 47-54 (2014). DOI: 10.15352/bjma/1381782086

Abstract

An operator $T \in B( \mathcal{H}) $ is called $k$-quasi-$\ast$-class A if $T^{\ast k}(|T^{2}|-|T^{\ast}|^{2})T^{k} \geq 0$ for a positive integer $k$, which is a common generalization of $\ast$-class A and quasi-$\ast$-class A. In this paper, firstly we prove some inequalities of this class of operators; secondly we consider the tensor products for $k$-quasi-$\ast$-class A operators, giving a necessary and sufficient condition for $T\otimes S$ to be a $k$-quasi-$\ast$-class A operator when $T$ and $S$ are both non-zero operators; at last we prove that the spectrum is continuous on the class of all $k$-quasi-$\ast$-class A operators.

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Fugen Gao. Xiaochun Li. "Tensor products and the spectral continuity for $k$-quasi-$\ast$-class A operators." Banach J. Math. Anal. 8 (1) 47 - 54, 2014. https://doi.org/10.15352/bjma/1381782086

Information

Published: 2014
First available in Project Euclid: 14 October 2013

zbMATH: 1275.47046
MathSciNet: MR3161681
Digital Object Identifier: 10.15352/bjma/1381782086

Subjects:
Primary: 47A63
Secondary: 47B20

Keywords: $k$-quasi-$\ast$-class A , spectral continuity , tensor product

Rights: Copyright © 2014 Tusi Mathematical Research Group

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