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Proceedings of the American Mathematical Society

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

 

 

The operator inequality $ P\leq A\sp *PA$


Author: B. P. Duggal
Journal: Proc. Amer. Math. Soc. 109 (1990), 697-698
MSC: Primary 47B15; Secondary 47A62, 47B20
DOI: https://doi.org/10.1090/S0002-9939-1990-1007495-7
MathSciNet review: 1007495
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Abstract: A short proof of the result that if $ P$ is a positive compact operator and $ A$ is a contraction such that $ p \leq {A^*}PA$, then $ P = {A^*}PA,\overline {\operatorname{ran} } P$ reduces $ A$ and $ A\vert\overline {\operatorname{ran} } P$ is unitary is given.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1007495-7
Keywords: Contraction, positive compact operator, hyponormal operator
Article copyright: © Copyright 1990 American Mathematical Society