Multiplication operators on weighted Banach spaces of a tree
Bull. Korean Math. Soc. 2017 Vol. 54, No. 3, 747-761
Published online May 13, 2017
Printed May 31, 2017
Robert F. Allen and Isaac M. Craig
University of Wisconsin-La Crosse, University of Wisconsin-La Crosse
Abstract : We study multiplication operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm. In addition, we determine the spectrum of the bounded multiplication operators and characterize the isometries. Finally, we study the multiplication operators between the weighted Banach spaces and the Lipschitz space by characterizing the bounded and the compact operators, determining estimates on the operator norm, and showing there are no isometries.
Keywords : multiplication operators, trees, weighted Banach space
MSC numbers : Primary 47B38, 05C05
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