Operator monotone functions, positive definite kernels and majorization
- Autores: Mitsuru Uchiyama
- Localización: Proceedings of the American Mathematical Society, ISSN 0002-9939, Vol. 138, Nº 11, 2010, págs. 3985-3996
- Idioma: inglés
- DOI: 10.1090/s0002-9939-10-10386-4
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Resumen
Let be a real continuous function on an interval, and consider the operator function defined for Hermitian operators . We will show that if is increasing w.r.t. the operator order, then for the operator function is convex. Let and be functions defined on an interval . Suppose is non-decreasing and is increasing. Then we will define the continuous kernel function by , which is a generalization of the Löwner kernel function. We will see that it is positive definite if and only if whenever for Hermitian operators , and we give a method to construct a large number of infinitely divisible kernel functions.
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