IJPAM: Volume 107, No. 3 (2016)

SKEW N-NORMAL COMPOSITION AND
WEIGHTED COMPOSITION OPERATORS ON $L^{2}(\mu)$

Anuradha Gupta$^1$, Renu Chugh$^2$, Jagjeet Jakhar$^3$
$^1$Department of Mathematics
Delhi College of Arts and Commerce
University of Delhi
Delhi, 110023, INDIA
$^{2,3}$Department of Mathematics
M.D. University
Rohtak, 124001, Haryana, INDIA


Abstract. An operator $T$ is called skew n-normal operator if
$(T^{n}T^{*})T = T(T^{*}T^{n})$, for all natural number n. In this paper, the condition under which composition operators and weighted composition operators become skew n-normal operators have been obtained in terms of radon-nikodym derivative $h_{n}$. We investigate some basic properties of such operators and study the relation among non normal composition operators and the skew n-normal composition operators.

Received: January 18, 2016

AMS Subject Classification: 47B33, 47B20, 46C05

Key Words and Phrases: composition operators, weighted composition operators, normal operator, quasi-normal operator, n-normal operator, skew n-normal operator

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DOI: 10.12732/ijpam.v107i3.11 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 107
Issue: 3
Pages: 625 - 634


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