On reducibility of weighted composition operators

Authors

  • M. R. Azimi Department of Mathematics, University of Maragheh, Maragheh, Iran.
  • M. R. Jabbarzadeh faculty of mathematical sciences, university of tabriz, p. o. box: 5166615648, tabriz,
  • M. ‎Jafari Bakhshkandi faculty of mathematical sciences, university of tabriz, p. o. box: 5166615648, tabriz,
Abstract:

In this paper, we study two types of the reducing subspaces for the weighted composition operator $W: frightarrow ucdot fcirc varphi$ on $L^2(Sigma)$. A necessary and sufficient condition is given for $W$ to possess the reducing subspaces of the form $L^2(Sigma_B)$ where $Bin Sigma_{sigma(u)}$. Moreover, we pose some necessary and some sufficient conditions under which the subspaces of the form $L^2(mathcal{A})$ reduce $W$. All of these are basically discussed by using the conditional expectation properties. To explain the results some examples are then presented.

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Journal title

volume 43  issue 3

pages  875- 883

publication date 2017-06-30

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