assures for , , with
Proc. Amer. Math. Soc. 101 (1987), 85-88
Primary 47A60; Secondary 15A45, 47B15
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Abstract: An operator means a bounded linear operator on a Hilbert space. This paper proves the assertion made in its title. Theorem 1 yields the famous result that assures for each when we put in Theorem 1. Also Corollary 1 implies that assures for each and this inequality for is just an affirmative answer to a conjecture posed by Chan and Kwong. We cite three counterexamples related to Theorem 1 and Corollary 1.
N. Chan and Man
Kam Kwong, Hermitian matrix inequalities and a conjecture,
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(46 #6078), http://dx.doi.org/10.1090/S0002-9939-1972-0306957-4
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