Banach Journal of Mathematical Analysis

Tensor products and the spectral continuity for $k$-quasi-$\ast$-class A operators

Fugen Gao and Xiaochun Li

Full-text: Open access

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.

Article information

Source
Banach J. Math. Anal., Volume 8, Number 1 (2014), 47-54.

Dates
First available in Project Euclid: 14 October 2013

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1381782086

Digital Object Identifier
doi:10.15352/bjma/1381782086

Mathematical Reviews number (MathSciNet)
MR3161681

Zentralblatt MATH identifier
1275.47046

Subjects
Primary: 47A63: Operator inequalities
Secondary: 47B20: Subnormal operators, hyponormal operators, etc.

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

Citation

Gao, Fugen; Li, Xiaochun. Tensor products and the spectral continuity for $k$-quasi-$\ast$-class A operators. Banach J. Math. Anal. 8 (2014), no. 1, 47--54. doi:10.15352/bjma/1381782086. https://projecteuclid.org/euclid.bjma/1381782086


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