Löwner inequality of indefinite type

✍ Scribed by T. Ando

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 173 KB
• Volume: 385
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(03)00496-8

✦ Synopsis

A selfadjoint involutive matrix J provides C n with an (indefinite) inner product [x, y] ≡ J x, y . For a pair of J -selfadjoint matrices A, B, the J -order relation

We will show that if A, B are J -selfadjoint matrices such that all eigenvalues of A, B are real and contained in an interval (α, β) then, for any operator monotone function f (t) on (α, β), the matrices f (A), f (B) are well defined by the Riesz-Dunford integral and