On the sum of two subnormal kernels
| Autor: | Soumitra Ghara, Surjit Kumar |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Class (set theory)
Pure mathematics Conjecture Applied Mathematics 010102 general mathematics Hilbert space Positive-definite matrix 01 natural sciences 010101 applied mathematics symbols.namesake Multiplication operator symbols Multiplication 0101 mathematics Unit (ring theory) Analysis Mathematics Reproducing kernel Hilbert space |
| Zdroj: | Journal of Mathematical Analysis and Applications. 469:1015-1027 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2018.09.048 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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