A condition under which 𝐵=𝐴=𝑈*𝐵𝑈 follows from 𝐵≤𝐴≤𝑈*𝐵𝑈

Okayasu, Takateru; Ueta, Yasunori

doi:10.1090/S0002-9939-06-08595-9

A condition under which $B=A=U^BU$ follows from $B\le A\le U^BU$
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by Takateru Okayasu and Yasunori Ueta PDF

Proc. Amer. Math. Soc. 135 (2007), 1399-1403 Request permission

Abstract:

We will give some sufficient conditions for a $p$-hyponormal operator, $p>0$, to be normal, and a sufficient condition for a triplet of operators $A$, $B$, $U$ with $A$, $B$ self-adjoint and $U$ unitary such that $B\le A\le U^*BU$ necessarily satisfies $B=A=U^*BU$.

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