Subnormality and Weighted Composition Operators on L2 Spaces

• Journal title : Kyungpook mathematical journal
• Volume 55, Issue 2,  2015, pp.345-353
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2015.55.2.345
Title & Authors
Subnormality and Weighted Composition Operators on L2 Spaces

Abstract
Subnormality of bounded weighted composition operators on $\small{L^2({\Sigma})}$ of the form $\small{Wf=uf{\circ}T}$, where T is a nonsingular measurable transformation on the underlying space X of a $\small{{\sigma}}$-finite measure space (X, $\small{{\Sigma}}$, $\small{{\mu}}$) 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 $\small{\{J_n(x)\}^{+{\infty}}_{n=0}}$ is a moment sequence for almost every $\small{x{{\in}}X}$, where $\small{J_n=h_nE_n({\mid}u{\mid}^2){\circ}T^{-n}}$, $\small{h_n=d{\mu}{\circ}T^{-n}/d{\mu}}$ and $\small{E_n}$ is the conditional expectation operator with respect to $\small{T^{-n}{\Sigma}}$.
Keywords
Subnormal;Weighted composition operators;Conditional expectation;Moment sequence;
Language
English
Cited by
1.
Quasinormal extensions of subnormal operator-weighted composition operators in ℓ 2 -spaces, Journal of Mathematical Analysis and Applications, 2017, 452, 1, 27
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