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http://dx.doi.org/10.4134/BKMS.2005.42.2.369

WEIGHTED COMPOSITION OPERATORS BETWEEN LP-SPACES  

JABBARZADEH, M.R. (DEPARTMENT OF MATHEMATICS, UNIVERSITY OF TABRIZ)
Publication Information
Bulletin of the Korean Mathematical Society / v.42, no.2, 2005 , pp. 369-378 More about this Journal
Abstract
In this paper we will consider the weighted composition operator $W=uC_{\varphi}$ between two different $L^p(X,\;\Sigma,\;\mu)$ spaces, generated by measurable and non-singular transformations $\varphi$ from X into itself and measurable functions u on X. We characterize the functions u and transformations $\varphi$ that induce weighted composition operators between $L^p-spaces$ by using some properties of conditional expectation operator, pair $(u,\;\varphi)$ and the measure space $(X,\;\Sigma,\;\mu)$. Also, Fredholmness of these type operators will be investigated.
Keywords
weighted composition operator; conditional expectation; multiplication operator; Fredholm operator;
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