Results 1 to 10 of about 60 (47)
Another consequence of tanahashi’s argument on best possibility of the grand Furuta inequality
Open Mathematics, 2013 Abstract We show that Tanahashi’s argument on best possibility of the grand Furuta inequality has an additional consequence.
Koizumi Tatsuya, Watanabe Keiichi
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Grand Furuta inequality and its variant [PDF]
Journal of Mathematical Inequalities, 2007 The grand Furuta inequality (GFI) is understood as follows: If positive operators A and B on a Hilbert space satisfy A B 0,A is invertible and t ∈ (0,1) ,t hen A 1−t+r (A r (A − t B p A − t ) s A r ) 1 t+r (pt)s+r holds for p, s 1a ndr t . In this note, we present a short proof of (GFI) which is done by the usual induction on s and the use of the ...
Ritsuo Nakamoto +2 more
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On the range of the parameters for the grand Furuta inequality to be valid II [PDF]
Journal of Mathematical Inequalities, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Keiichi Watanabe
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Generalization of the Kantorovich type operator inequalities via Grand Furuta inequality [PDF]
Mathematical Inequalities and Applications, 2006 In this note we show the characterization of the $\delta$-order by means of a generalized Kantorovich constant via Grand Furuta inequality, which is an extension result of that from M.Fujii, E.Kamei, Y.Seo, {; ; \it Kantorovich type operator inequalities via grand Furuta inequality}; ; , Sci.\ Math., {; ; \bf 3}; ; (2000), 263--272.
Josip Pecaric
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A short proof of the best possibility for the grand Furuta inequality
Journal of Inequalities and Applications, 1999 In this note, we give a short proof to the best possibility for the grand Furuta inequality: for given , , , and , there exist positive invertible operators and such that and
Matsumoto Akemi +2 more
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Reverse of the grand Furuta inequality and its applications
Banach Journal of Mathematical Analysis, 2008 Let \(A, B \geq 0\) be bounded operators acting on a Hilbert space. It is well-known that there are close relations between the Furuta inequality and the Kantorovich inequality: the Kantorovich inequality is often used to give the reverse inequalities of Furuta type inequalities.
Ritsuo Nakamoto +2 more
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Operator functions associated with the grand Furuta inequality [PDF]
Mathematical Inequalities and Applications, 1998 Summary: We discuss the monotonicity of operator functions associated with the grand Furuta inequality, some of which are considered under the chaotic order \(\log A\geq\log B\). In some restricted cases, several known operator inequalities related to the Furuta inequality will appear as corollaries of our results.
Masatoshi Fujii, Eizaburo Kamei
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A satellite of the grand Furuta inequality and its application
Linear Algebra and Its Applications, 2013 Let \(A,B\) be bounded linear operators acting on a Hilbert space, \(A \geq B >0\), \(t \in[0,1]\), \(r \geq t\) and \(p, s \geq 1\). The well-known Grand Furuta (GF) inequality says that \[ A^{-r+t}\sharp_{\frac{1-t+r}{(p-t)s+r}} (A^{t}\natural_s B^p) \leq A \] (cf.\ \textit{T. Furuta} [Linear Algebra Appl. 219, 139--155 (1995; Zbl 0822.15008)]).
Ritsuo Nakamoto, Masatoshi Fujii
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Mean theoretic approach to a further extension of grand Furuta inequality [PDF]
Journal of Mathematical Inequalities, 2010 Very recently, Furuta has shown a further extension of grand Furuta inequality. In this paper, we obtain a more precise and clear expression of Furuta's extension by considering a mean theoretic proof of grand Furuta inequality. Moreover, we get a variant of Furuta's extension by scrutinizing the former argument.
Eizaburo Kamei
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Matrix inequalities including grand Furuta inequality via Karcher mean [PDF]
Journal of Mathematical Inequalities, 2014 In our previous paper, we have shown a generalization of Furuta inequality via Karcher mean (Riemannian mean) by using Yamazaki's results which are generalizations of Ando-Hiai inequality and related ones. In this paper, we shall show a generalization of grand Furuta in- equality as an extension of our previous result.
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