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- W2034656692 abstract "We give two types of niixed Hadamard inequalities containing the terms T, ITI, and IT* , where T is a bounded linear operator on a complex Hilbert space. As an immediate consequence of these results, we can easily show some extensions of the Hadamard inequality and also the Heinze inequality: (*) ~ ~~~~ I(Tx,y) 12 < (IT 12a,x )(IT* 12 (1 ,) Y y) for any T, any x,y in H, and any real number a with 0 < a < 1. And the following conditions are equivalent in case 0 < a < 1: (1) the equality in (*) holds; (2) IT12,x and T*y are linearly dependent; (3) Tx and IT*12(1-a)y are linearly dependent. Results in this paper would remain valid for unbounded operators under slight modifications." @default.
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- W2034656692 date "1988-01-01" @default.
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- W2034656692 title "Two mixed Hadamard type generalizations of Heinz inequality" @default.
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