J. Korean Math. Soc. 2004; 41(1): 95-105
Printed January 1, 2004
Copyright © The Korean Mathematical Society.
M. R. Jabbarzadeh
University of Tabriz
In this paper we will consider the weighted composition operators $W=uC_\tau$ between $L^p(X,\Sigma, \mu)$ spaces and Orlicz spaces $L^\varphi(X,\Sigma,\mu)$, generated by measurable and non-singular transformations $\tau$ from $X$ into itself and measurable functions $u$ on $X$. We characterize the functions $u$ and transformations $\tau$ that induce weighted composition operators between $L^p$-spaces by using some properties of conditional expectation operator, pair ($u$, $\tau$) and the measure space $(X,\Sigma,\mu)$. Also, some other properties of these types of operators will be investigated.
Keywords: weighted composition operator, conditional expectation, Fredholm operator, Orlicz space
MSC numbers: Primary 47B20, 47B33; Secondary 47B38, 46E30
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