Some operator monotone functions
- 1 January 1972
- journal article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 36 (1) , 309
- https://doi.org/10.1090/s0002-9939-1972-0306957-4
Abstract
A short proof is given based on <!-- MATH ${C^ \ast }$ --> -algebra theory for the well-known theorem that if S and T are bounded selfadjoint operators on a Hilbert space such that <!-- MATH $0 \leqq S \leqq T$ --> then <!-- MATH ${S^\alpha } \leqq {T^\alpha }$ --> for each <!-- MATH $0 \leqq \alpha \leqq 1$ --> .
Keywords
This publication has 2 references indexed in Scilit:
- A Theorem on Operator AlgebrasHiroshima Mathematical Journal, 1955
- ber monotone MatrixfunktionenMathematische Zeitschrift, 1934