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Chebyshev type inequalities for functions of selfadjoint operators
 in Hilbert spaces, Linear and Multilinear Algebra 58 (2010
"... Abstract. Some inequalities for continuous synchronous (asynchronous) functions of selfadjoint linear operators in Hilbert spaces, under suitable assumptions for the involved operators, are given. 1. ..."
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Abstract. Some inequalities for continuous synchronous (asynchronous) functions of selfadjoint linear operators in Hilbert spaces, under suitable assumptions for the involved operators, are given. 1.
OPERATOR EXTENSIONS OF HUA’S INEQUALITY
, 810
"... Abstract. We give an extension of Hua’s inequality in preHilbert C ∗modules without using convexity or the classical Hua’s inequality. As a consequence, some known and new generalizations of this inequality are deduced. Providing a Jensen inequality in the content of Hilbert C ∗modules, another e ..."
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Cited by 7 (4 self)
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Abstract. We give an extension of Hua’s inequality in preHilbert C ∗modules without using convexity or the classical Hua’s inequality. As a consequence, some known and new generalizations of this inequality are deduced. Providing a Jensen inequality in the content of Hilbert C ∗modules, another extension of Hua’s inequality is obtained. We also present an operator Hua’s inequality, which is equivalent to operator convexity of given continuous real function. 1.
OSTROWSKI’S TYPE INEQUALITIES FOR CONTINUOUS FUNCTIONS OF SELFADJOINT OPERATORS ON HILBERT SPACES: A SURVEY OF RECENT RESULTS
, 2011
"... In this survey we present some recent results obtained by the author in extending Ostrowski inequality in various directions for continuous functions of selfadjoint operators defined on complex Hilbert spaces. ..."
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Cited by 3 (0 self)
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In this survey we present some recent results obtained by the author in extending Ostrowski inequality in various directions for continuous functions of selfadjoint operators defined on complex Hilbert spaces.
INEQUALITIES FOR THE ČEBYŠEV FUNCTIONAL OF TWO FUNCTIONS OF SELFADJOINT OPERATORS IN HILBERT SPACES
"... ABSTRACT. Some recent inequalities for the Čebyšev functional of two functions of selfadjoint linear operators in Hilbert spaces, under suitable assumptions for the involved functions and ..."
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Cited by 1 (1 self)
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ABSTRACT. Some recent inequalities for the Čebyšev functional of two functions of selfadjoint linear operators in Hilbert spaces, under suitable assumptions for the involved functions and
Right Type Departmental Bulletin Paper
"... An extension of Kantorovich inequality to $n$operators (Takeaki Yamazaki) Kanagawa University In this report, we shall extend Kantorovich inequality. This is an estimate by using the geometric mean of $n$operators which have been defined by AndoLiMathias in [1]. As a related result, we obtain a ..."
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An extension of Kantorovich inequality to $n$operators (Takeaki Yamazaki) Kanagawa University In this report, we shall extend Kantorovich inequality. This is an estimate by using the geometric mean of $n$operators which have been defined by AndoLiMathias in [1]. As a related result, we obtain a reverse inequality of arithmeticgeometric means one of $n$operators via Kantorovich constant. Moreover, we give a formula of geometric mean of $n$touples of 2by2 matrices with a $\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{e} $ condition, and we shall obtain more precise results of extended Kantorovich inequality in case 2by2 matrices case. This is based on the following preprint: [Yl T. Yam azaki, An extension of Kantorovich inequality to $n $operators via the geometric mean by AndoLiMathias, preprint. 1.
FURTHER EXTENSIONS OF CHARACTERIZATIONS OF CHAOTIC ORDER ASSOCIATED WITH KANTOROVICH TYPE INEQUALITIES
, 2000
"... Abstract. We showed characterizations of chaotic order via Kantorovich inequality in our previous paper. Recently as a nice application of generalized Furuta inequality, Furuta and Seo showed an extension of one of our results and a related result on operator equations. In this paper, by using esse ..."
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Abstract. We showed characterizations of chaotic order via Kantorovich inequality in our previous paper. Recently as a nice application of generalized Furuta inequality, Furuta and Seo showed an extension of one of our results and a related result on operator equations. In this paper, by using essentially the same idea as theirs, we shall show further extensions of both their results and the following our another previous result which is a characterization of chaotic order via Specht's ratio. "Let A and B be positive invertible operators satisfying
Inequalities of Furuta and . . . Hadamard Product
 J. OF LNEQUAL. & APPL., 2000, VOL. 5, PP. 263285
, 2000
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