Positive Hankel operators, positive definite kernels and related topics
| Autor: | Piotr Niemiec |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
operator range
Pure mathematics Primary 47B35 Secondary 46E22 47B25 0211 other engineering and technologies 02 engineering and technology Positive-definite matrix 01 natural sciences symbols.namesake Operator (computer programming) Hankel operator FOS: Mathematics 0101 mathematics positive operator Mathematics double positivity condition Algebra and Number Theory 010102 general mathematics Spectrum (functional analysis) Hilbert space positive square root 021107 urban & regional planning Operator theory Functional Analysis (math.FA) positive definite kernel Mathematics - Functional Analysis Bounded function Isometry symbols Analysis Kernel (category theory) |
| Zdroj: | Advances in Operator Theory. 5:950-993 |
| ISSN: | 2538-225X 2662-2009 |
| DOI: | 10.1007/s43036-020-00058-6 |
| Popis: | It is shown that a positive (bounded linear) operator on a Hilbert space with trivial kernel is unitarily equivalent to a Hankel operator that satisfies double positivity condition if and only if it is non-invertible and has simple spectrum (that is, if this operator admits a cyclic vector). More generally, for an arbitrary positive (bounded linear) operator A on a Hilbert space H with trivial kernel the collection V(A) of all linear isometries V from H into H such that AV is positive as well is investigated. In particular, operators A such that V(A) contains a pure isometry with a given deficiency index are characterized. Some applications to unbounded positive self-adjoint operators as well as to positive definite kernels are presented. In particular, positive definite matrix-type square roots of such kernels are studied and kernels that have a unique such root are characterized. The class of all positive definite kernels that have at least one such a square root is also investigated. 35 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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