Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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 $0 \leqq \alpha \leqq 1$.
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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