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http://dx.doi.org/10.5666/KMJ.2015.55.2.345

Subnormality and Weighted Composition Operators on L2 Spaces  

AZIMI, MOHAMMAD REZA (Department of Mathematics, Faculty of Sciences, University of Maragheh)
Publication Information
Kyungpook Mathematical Journal / v.55, no.2, 2015 , pp. 345-353 More about this Journal
Abstract
Subnormality of bounded weighted composition operators on $L^2({\Sigma})$ of the form $Wf=uf{\circ}T$, where T is a nonsingular measurable transformation on the underlying space X of a ${\sigma}$-finite measure space (X, ${\Sigma}$, ${\mu}$) and u is a weight function on X; is studied. The standard moment sequence characterizations of subnormality of weighted composition operators are given. It is shown that weighted composition operators are subnormal if and only if $\{J_n(x)\}^{+{\infty}}_{n=0}$ is a moment sequence for almost every $x{{\in}}X$, where $J_n=h_nE_n({\mid}u{\mid}^2){\circ}T^{-n}$, $h_n=d{\mu}{\circ}T^{-n}/d{\mu}$ and $E_n$ is the conditional expectation operator with respect to $T^{-n}{\Sigma}$.
Keywords
Subnormal; Weighted composition operators; Conditional expectation; Moment sequence;
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Times Cited By KSCI : 1  (Citation Analysis)
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