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Relations Between Two Operator Inequalities Motivated by the Theory of Operator Means

Authors:

Masatoshi Ito

Affiliation:

(1) Department of Mathematical Information Science, Tokyo University of Science, 1-3 Kagurazaka Shinjuku-ku, Tokyo 162-8601, Japan

Abstract:

We shall show several results on operator inequalities motivated by the theory of operator means. As a consequence of our main result, we shall also obtain relations between two operator inequalities

$f(B^{tfrac{1} {2}} AB^{tfrac{1} {2}} ) geq B{text{ and }}A geq g(A^{tfrac{1} {2}} BA^{tfrac{1} {2}} )$

for (not necessarily invertible) positive operators A and B, where f and g are non-negative continuous functions on [0,∞) satisfying f(t)g(t) = t.

Keywords:

KeywordHeading" >Mathematics Subject Classification (2000). Primary 47A63 47A64

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