Some operator monotone functions
Author:
Gert K. Pedersen
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
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Abstract | References | Similar Articles | Additional Information
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 $0 \leqq \alpha \leqq 1$.
- Jacques Dixmier, Les $C^{\ast } $-algĂšbres et leurs reprĂ©sentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Ăditeur-Imprimeur, Paris, 1964 (French). MR 0171173
- Karl Löwner, Ăber monotone Matrixfunktionen, Math. Z. 38 (1934), no. 1, 177â216 (German). MR 1545446, DOI https://doi.org/10.1007/BF01170633
- TĂŽzirĂŽ Ogasawara, A theorem on operator algebras, J. Sci. Hiroshima Univ. Ser. A 18 (1955), 307â309. MR 73955
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Additional Information
Keywords:
Operator monotone functions,
<!â MATH ${C^ \ast }$ â> <IMG WIDTH="31" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${C^ \ast }$">-algebras,
positive operators
Article copyright:
© Copyright 1972
American Mathematical Society
