Mixed Hadamard’s theorems
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- by Takayuki Furuta PDF
- Proc. Amer. Math. Soc. 96 (1986), 217-220 Request permission
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 $T,\left | T \right |$ and $\left | {{T^ * }} \right |$ as extensions of Hadamard’s theorem and mixed Schwarz’s inequality ${\left | {(Tx,y)} \right |^2} \leq (\left | T \right |x,x)(\left | {{T^ * }} \right |y,y)$ 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
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 217-220
- MSC: Primary 47A05; Secondary 47A30
- DOI: https://doi.org/10.1090/S0002-9939-1986-0818447-0
- MathSciNet review: 818447