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,
Amer. Math. Monthly 92 (1985), no. 8, 533–541.
Hansen, An operator inequality, Math. Ann.
246 (1979/80), no. 3, 249–250. MR 563403
K. Pedersen, Some operator monotone
functions, Proc. Amer. Math. Soc. 36 (1972), 309–310. MR 0306957
(46 #6078), http://dx.doi.org/10.1090/S0002-9939-1972-0306957-4
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