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Complementary inequalities of the Furuta inequality (Operator Inequalities and related topics)
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Generalizations of Furuta's inequality
Linear and Multilinear Algebra, 2013We obtain amongst others the following result for any x, y ∈ H, where is a function defined by power series with real coefficients and convergent on the open disk D(0, R) ⊂ ℂ, R > 0, , T ∈ ℬ(H), α, β ≥ 0 with α + β ≥ 1 and ‖T ‖2α, ‖T‖2β
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Complements to the Furuta inequality. IV
1997Summary: Complementary results to the Furuta inequality are given in cases of positive invertible operators as a continuation of our previous results in part I, II, III which are generalizations of results in parts I and II [Zbl 0818.47012 and Zbl 0887.47016] and improvements of results in part III [\textit{T.
Fujii, Masatoshi +2 more
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Complementary inequalities of the Furuta inequality
1999The \(\alpha\)-power mean of two operators \(A\) and \(B\) is defined by \(A\#_\alpha B= A^{1/2}(A^{-1/2} BA^{-1/2})^\alpha A^{1/2}\) for \(\alpha\in [0,1]\); cf. \textit{F. Kubo} and \textit{T. Ando} [Math. Ann. 246, 205-224 (1980; Zbl 0421.47011)]. The Furuta inequality, which is a refinement of the Lövner-Heinz inequality asserts that if \(A\geq B ...
Fujii, Masatoshi +2 more
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An Application of Furuta’s Inequality to Ando’s Theorem
1992Several authors have given mean theoretic considerations to Furuta’s inequality which is an extension of Lowner-Heinz inequality. Ando discussed it on the geometric mean. In this note, Furuta’s inequality is applied to a generalization of Ando’s theorem.
Masatoshi Fujii +2 more
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