New York Journal of Mathematics
Volume 20 (2014) 711-726


Valentin Matache

Isometric weighted composition operators

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Published: August 6. 2014
Keywords: Weighted composition operator, isometry, numerical range.
Subject: 47B33, 47A12

A composition operator is an operator on a space of functions defined on the same set. Its action is by composition to the right with a fixed selfmap of that set. A composition operator followed by a multiplication operator is called a weighted composition operator. In this paper, we study when weighted composition operators on the Hilbert Hardy space of the open unit disc are isometric. We find their Wold decomposition in select cases and apply it to the computation of numerical ranges.

Author information

Department of Mathematics, University of Nebraska, Omaha, NE 68182, USA.