On the sum of two subnormal kernels

Ghara, Soumitra and Kumar, Surjit (2018) On the sum of two subnormal kernels. In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 469 (2). pp. 1015-1027.

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Abstract

We show, by means of a class of examples, that if K-1 and K-2 are two positive definite kernels on the unit disc such that the multiplication by the coordinate function on the corresponding reproducing kernel Hilbert space is subnormal, then the multiplication operator on the Hilbert space determined by their sum K-1 + K-2 need not be subnormal. This settles a recent conjecture of Gregory T. Adams, Nathan S. Feldman and Paul J. McGuire in the negative. We also discuss some cases for which the answer is affirmative. (C) 2018 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Publication:	JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Publisher:	ACADEMIC PRESS INC ELSEVIER SCIENCE
Additional Information:	Copy right for this article belong to ACADEMIC PRESS INC ELSEVIER SCIENCE
Keywords:	Completely alternating; Completely hyperexpansive; Completely monotone; Positive definite kernel; Spherically balanced spaces; Subnormal operators
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	16 Nov 2018 15:33
Last Modified:	16 Nov 2018 15:33
URI:	http://eprints.iisc.ac.in/id/eprint/61083

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