Antitonicity of the inverse for selfadjoint matrices, operators, and relations

Autor:	Behrndt, J., Hassi, S., de Snoo, H. S. V., Wietsma, H. L.
Rok vydání:	2014
Předmět:	Mathematics - Functional Analysis Primary 47A06 47A63 47B25 Secondary 15A09 15A45 15B57
Druh dokumentu:	Working Paper
Popis:	Let $H_1$ and $H_2$ be selfadjoint operators or relations (multivalued operators) acting on a separable Hilbert space and assume that the inequality $H_1 \leq H_2$ holds. Then the validity of the inequalities $-H_1^{-1} \leq -H_2^{-1}$ and $H_2^{-1} \leq H_1^{-1}$ is characterized in terms of the inertia of $H_1$ and $H_2$. Such results are known for matrices and boundedly invertible operators. In the present paper those results are extended to selfadjoint, in general unbounded, not necessarily boundedly invertible, operators and, more generally, for selfadjoint relations in separable Hilbert spaces. Comment: To appear in Proc. Amer. Math. Soc.; 13 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1403.5704 Zobrazit plný text záznamu View this record from Arxiv