Some operator monotone functions
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- by Gert K. Pedersen
- Proc. Amer. Math. Soc. 36 (1972), 309-310
- DOI: https://doi.org/10.1090/S0002-9939-1972-0306957-4
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Abstract:
A short proof is given based on ${C^ \ast }$-algebra theory for the well-known theorem that if S and T are bounded selfadjoint operators on a Hilbert space such that $0 \leqq S \leqq T$ then ${S^\alpha } \leqq {T^\alpha }$ for each $0 \leqq \alpha \leqq 1$.References
- Jacques Dixmier, Les $C^{\ast }$-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris, 1964 (French). MR 0171173
- Karl Löwner, Über monotone Matrixfunktionen, Math. Z. 38 (1934), no. 1, 177–216 (German). MR 1545446, DOI 10.1007/BF01170633
- Tôzirô Ogasawara, A theorem on operator algebras, J. Sci. Hiroshima Univ. Ser. A 18 (1955), 307–309. MR 73955
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 309-310
- MSC: Primary 47B15
- DOI: https://doi.org/10.1090/S0002-9939-1972-0306957-4
- MathSciNet review: 0306957