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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
DOI: https://doi.org/10.1090/S0002-9939-1972-0306957-4
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 $0 \leqq \alpha \leqq 1$.


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Keywords: Operator monotone functions, <!– MATH ${C^ \ast }$ –> <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