On sum of two subnormal kernels

Soumitra Ghara; Surjit Kumar

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arXiv · 1703.02792

On sum of two subnormal kernels

Soumitra Ghara·Surjit Kumar

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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.

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BibTeX RIS

Soumitra Ghara, Surjit Kumar. 2017-03-08. On sum of two subnormal kernels. https://arxiv.org/abs/1703.02792

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