Mixed Hadamard's Theorems

Furuta, Takayuki

doi:10.2307/2046156

Proceedings of the American Mathematical Society

1986

DOI: 10.2307/2046156

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Mixed Hadamard's Theorems

Takayuki Furuta¹

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1988

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Two mixed Hadamard type generalizations of Heinz inequality

Furuta¹

1988

Proc. Amer. Math. Soc.

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Dedicatedto Professor Zirô Takeda on his 65th birthday with respect and affection ABSTRACT. We give two types of mixed Hadamard inequalities containing the terms T, \T\, and |T*|, where T is a bounded linear operator on a complex Hubert space. As an immediate consequence of these results, we can easily show some extensions of the Hadamard inequality and also the Heinze inequality: M \(Tx,y)\2 < (\T\2ax,x)(.\T*\2^-"îy,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) |T|2ai and T'y are linearly dependent; (3) Tx and \T*\2(l~a}y are linearly dependent. Results in this paper would remain valid for unbounded operators under slight modifications.

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Two mixed Hadamard type generalizations of Heinz inequality

Furuta¹

1988

Proc. Amer. Math. Soc.

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Mixed Hadamard's Theorems

Cited by 1 publication

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Two mixed Hadamard type generalizations of Heinz inequality

Two mixed Hadamard type generalizations of Heinz inequality

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