Banach Journal of Mathematical Analysis

Compact operators in the commutant of essentially normal operators

F. B. Höseynov and H. S. Mustafayev

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Abstract

Let $T$ be a bounded, linear operator on a complex, separable, infinite dimensional Hilbert space $H$. We assume that $T$ is an essentially isometric (resp. normal) operator, that is, $I_{H}-T^{\ast }T$ (resp. $TT^{\ast }-T^{\ast }T)$ is compact. For the compactness of $S$ from the commutant of $T,$ some necessary and sufficient conditions are found on $S.$ Some related problems are also discussed.

Article information

Source
Banach J. Math. Anal., Volume 8, Number 2 (2014), 1-15.

Dates
First available in Project Euclid: 4 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1396640047

Digital Object Identifier
doi:10.15352/bjma/1396640047

Mathematical Reviews number (MathSciNet)
MR3189534

Zentralblatt MATH identifier
1320.47020

Subjects
Primary: 47A10: Spectrum, resolvent
Secondary: 47A53: (Semi-) Fredholm operators; index theories [See also 58B15, 58J20] 47A60: Functional calculus 47B07: Operators defined by compactness properties

Keywords
Compact operator essentially unitary (normal) operator (essential) spectrum functional calculus

Citation

Mustafayev, H. S.; Höseynov, F. B. Compact operators in the commutant of essentially normal operators. Banach J. Math. Anal. 8 (2014), no. 2, 1--15. doi:10.15352/bjma/1396640047. https://projecteuclid.org/euclid.bjma/1396640047


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