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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Some operator monotone functions

Author: Gert K. Pedersen
Journal: Proc. Amer. Math. Soc. 36 (1972), 309-310
MSC: Primary 47B15
MathSciNet review: 0306957
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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 [Enhancements On Off] (What's this?)

  • [1] J. Dixmier, Les $ {C^ \ast }$-algèbres et leurs représentations, Cahiers Scientifiques, fasc. 29, Gauthier-Villars, Paris, 1964. MR 30 #1404. MR 0171173 (30:1404)
  • [2] K. Löwner, Über monotone matrixfunctionen, Math. Z. 38 (1934), 177-216. MR 1545446
  • [3] T. Ogasawara, A theorem on operator algebras, J. Sci. Hiroshima Univ. Ser. A 18 (1955), 307-309. MR 17, 514. MR 0073955 (17:514a)

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Keywords: Operator monotone functions, $ {C^ \ast }$-algebras, positive operators
Article copyright: © Copyright 1972 American Mathematical Society

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