Annals of Functional Analysis

On class $\mathcal{A}(k^{*})$ operators

Naim L. Braha, Ilmi Hoxha, and Salah Mecheri

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Abstract

This paper deals with some classes of bounded linear operators on Hilbert spaces. The main emphasis is put onto the classes $\mathcal{A}(k^{*})$ and $\mathcal{A}_{(k^{*})}P,\, k>0$. Some additional results are given for other classes, like $P\mathcal{A}(k^{*})$, $M-\mathcal{A}(k^{*})$ and spectral properties of operators belonging to $\mathcal{A}(k^{*})$ are considered. We also describe under what conditions a matrix-operator $T_{A,B}$ belongs to $\mathcal{A}(k^{*})$, $\mathcal{A}_{(k^{*})}P$ or $P\mathcal{A}(k^{*})$.

Article information

Source
Ann. Funct. Anal., Volume 6, Number 4 (2015), 90-106.

Dates
First available in Project Euclid: 1 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.afa/1435764004

Digital Object Identifier
doi:10.15352/afa/06-4-90

Mathematical Reviews number (MathSciNet)
MR3365984

Zentralblatt MATH identifier
1320.47022

Subjects
Primary: 47B20: Subnormal operators, hyponormal operators, etc.
Secondary: 47A80: Tensor products of operators [See also 46M05] 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)

Keywords
$*$-paranormal operator $\mathcal{A}(k^{*})$-class operator $M-\mathcal{A}(k^{*})$-class operator absolute-$k^{*}$-paranormal

Citation

Braha, Naim L.; Hoxha, Ilmi; Mecheri, Salah. On class $\mathcal{A}(k^{*})$ operators. Ann. Funct. Anal. 6 (2015), no. 4, 90--106. doi:10.15352/afa/06-4-90. https://projecteuclid.org/euclid.afa/1435764004


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