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2013 Special operator classes and their properties
Mehmet Gurdal, Mubariz Tapdigoglu Karaev , Ulas Yamanci
Banach J. Math. Anal. 7(2): 74-85 (2013). DOI: 10.15352/bjma/1363784224


We introduce some special operator classes and study in terms of Berezin symbols their properties. In particular, we give some characterizations of compact operators and Schatten-von Neumann class operators in terms of Berezin symbols. We also consider some classes of compact operators on a Hilbert space $H,$ which are generalizations of the well known Schatten-von Neumann classes of compact operators. Namely, for any number $p \in (0,\infty)$ and the sequence $w:=(w_{n})_{n\geq0}$ of complex numbers $w_{n},$ $n\geq 0,$ we define the following classes of compact operators on $H $: $$S_{p}^{w}(H)=\left\{ K\in S_{\infty}(H):\sum_{n=0}^{\infty}(s_{n} (K))^{p}w_{n}^{p}\hbox{ is convergent series }\right\}, $$ where $s_{n}(K)$ denotes the $n$th singular number of the operator $K$. The characterizations of these classes are given in terms of Berezin symbols.


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Mehmet Gurdal. Mubariz Tapdigoglu Karaev . Ulas Yamanci . "Special operator classes and their properties." Banach J. Math. Anal. 7 (2) 74 - 85, 2013.


Published: 2013
First available in Project Euclid: 20 March 2013

zbMATH: 1277.47034
MathSciNet: MR3039940
Digital Object Identifier: 10.15352/bjma/1363784224

Primary: 47B35
Secondary: 47B10

Keywords: $s$-number , Abel convergence , Berezin symbol , Compact operator , Schatten-Von Neumann classes

Rights: Copyright © 2013 Tusi Mathematical Research Group


Vol.7 • No. 2 • 2013
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