English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $H_1$ and $H_2$ be selfadjoint operators or relations (multivaluedoperators) 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 theinertia of $H_1$ and $H_2$. Such results are known for matrices and boundedlyinvertible operators. In the present paper those results are extended toselfadjoint, in general unbounded, not necessarily boundedly invertible,operators and, more generally, for selfadjoint relations in separable Hilbertspaces.

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