Multiplication operators on weighted Banach spaces of a tree

Robert F. Allen; Isaac M. Craig

doi:10.4134/BKMS.b160007

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2017; 54(3): 747-761

Online first article May 13, 2017 Printed May 31, 2017

https://doi.org/10.4134/BKMS.b160007

Multiplication operators on weighted Banach spaces of a tree

Robert F. Allen and Isaac M. Craig

University of Wisconsin-La Crosse, University of Wisconsin-La Crosse

Abstract

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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