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Proceedings of the American Mathematical Society

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



Mixed Hadamard's theorems

Author: Takayuki Furuta
Journal: Proc. Amer. Math. Soc. 96 (1986), 217-220
MSC: Primary 47A05; Secondary 47A30
MathSciNet review: 818447
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Abstract: An operator $ T$ means a bounded linear operator on a complex Hilbert space $ H$. We give two types of mixed Hadamard's theorems containing the terms $ T,\left\vert T \right\vert$ and $ \left\vert {{T^ * }} \right\vert$ as extensions of Hadamard's theorem and mixed Schwarz's inequality $ {\left\vert {(Tx,y)} \right\vert^2} \leq (\left\vert T \right\vert x,x)(\left\vert {{T^ * }} \right\vert y,y)$ for any $ T$ and for any $ x$ and $ y$ in $ H$. Also we scrutinize the cases when the equalities in these mixed Hadamard's theorems hold.

References [Enhancements On Off] (What's this?)

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Keywords: Hadamard's theorem, Schwarz's inequality, polar decomposition
Article copyright: © Copyright 1986 American Mathematical Society