Characterization of Pure Contractive Multipliers and Applications

Sarkar, S (2022) Characterization of Pure Contractive Multipliers and Applications. In: Complex Analysis and Operator Theory, 16 (8).

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Abstract

A contraction T on a Hilbert space H is said to be pure if the sequence {T∗n}n converges to 0 in the strong operator topology. Motivated by this definition, an operator-valued multiplier Φ of a vector-valued reproducing kernel Hilbert space (rkHs) is said to be pure contractive if the associated multiplication operator MΦ is a pure contraction. In this article, we completely characterize pure contractive multipliers Φ (z) of several vector-valued rkHs’s on the polydisc Dn as well as the unit ball Bn in Cn, by proving that Φ (z) is pure contractive if and only if Φ (0) is a pure contraction on the underlying Hilbert space. The list of rkHs’s include well-studied Hilbert spaces like Hardy, Bergman, Dirichlet and Drury–Arveson spaces. Finally, we present some applications of our characterization of pure contractive multipliers associated with the polydisc.

Item Type:	Journal Article
Publication:	Complex Analysis and Operator Theory
Publisher:	Birkhauser
Additional Information:	The copyright for this article belongs to Birkhauser.
Keywords:	Bergman space; Dirichlet space; Hardy space; Isometric dilation; Left-invertible operators; Multipliers; Reproducing kernels
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	03 Jan 2023 04:54
Last Modified:	03 Jan 2023 04:54
URI:	https://eprints.iisc.ac.in/id/eprint/78660

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