# WEIGHTED COMPOSITION OPERATORS BETWEEN LP-SPACES

• Published : 2005.05.01
• 66 4

#### 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.ᘀࡠ궚䃨⨀磕ྈ肀Ѐ᠀܀䃨⨀᠀Ѐ쌛ܕ儁돐僧⨀ꣻ⨀ꣻ⨀儈돀룡⨀堘?⨀냑ʗ⨀⤈돐偦඗⨀偦඗⨀唀䩁䭏㈰〵〲㘳㜱㜱㠶㠀

#### Keywords

weighted composition operator;conditional expectation;multiplication operator;Fredholm operator

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#### Cited by

1. Basic properties of multiplication and composition operators between distinct Orlicz spaces vol.30, pp.2, 2017, https://doi.org/10.1007/s13163-016-0214-1