Operator extensions of Hua's inequality (original) (raw)

2009, Linear Algebra and its Applications

We give an extension of Hua's inequality in pre-Hilbert 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. G.-S. Yang and B.-K. Han extended this result for a finite sequence of complex numbers. C.E.M. Pearce and J.E. Pečarić [14] generalized Hua's inequality for real convex functions; see also [1]. S.S. Dragomir and G.-S. Yang [2] extended Hua's inequality in the setting of real inner product spaces by applying Hua's inequality for n = 1. Their result was generalized by 2000 Mathematics Subject Classification. Primary 47A63; secondary 46L08, 47B10, 47A30, 47B15, 26D07, 15A60.

Notes on some inequalities for Hilbert space operators

Publications of the Research Institute for Mathematical Sciences, 1988

Several inequalities for Hilbert space operators are extended. These include results of Furuta, Halmos, and Kato on the mixed Schwarz inequality, the generalized Reid inequality as proved by Halmos and a classical inequality in the theory of compact non-self-adjoint operators which is essentially due to Weyl. Some related inequalities are also discussed.

The Generalizations of Hilbert's Inequality

International Journal of Mathematics and Mathematical Sciences, 2008

By introducing some parameters and estimating the weight functions, we establish a new Hilberttype inequalities with best constant factors. The equivalent inequalities are also considered.

A variant of Jensen’s inequality of Mercer’s type for operators with applications

Linear Algebra and Its Applications, 2006

A variant of Jensen’s operator inequality for convex functions, which is a generalization of Mercer’s result, is proved. Obtained result is used to prove a monotonicity property for Mercer’s power means for operators, and a comparison theorem for quasi-arithmetic means for operators.

Advances in Operator Cauchy--Schwarz inequalities and their reverses

Annals of Functional Analysis, 2015

The Cauchy-Schwarz (C-S) inequality is one of the most famous inequalities in mathematics. In this survey article, we first give a brief history of the inequality. Afterward, we present the C-S inequality for inner product spaces. Focusing on operator inequalities, we then review some significant recent developments of the C-S inequality and its reverses for Hilbert space operators and elements of Hilbert C *-modules. In particular, we pay special attention to an operator Wielandt inequality.

A treatment of the Cauchy–Schwarz inequality in -modules

Journal of Mathematical Analysis and Applications, 2011

We study the Cauchy-Schwarz and some related inequalities in a semi-inner product module over a C * -algebra A . The key idea is to consider a semi-inner product A -module as a semi-inner product A -module with respect to another semi-inner product. In this way, we improve some inequalities such as the Ostrowski inequality and an inequality related to the Gram matrix. The induced semi-inner products are also related to the the notion of covariance and variance. Furthermore, we obtain a sequence of nested inequalities that emerges from the Cauchy-Schwarz inequality. As a consequence, we derive some interesting operator-theoretical corollaries. In particular, we show that the sequence arising from our construction, when applied to a positive invertible element of a C * -algebra, converges to its inverse. 1 2 , where the latter norm denotes that in the C * -algebra A . A pre-Hilbert A -module (or an inner-product module) is a semi-inner product module over A in which · defined as above

The generalized of Selberg’s inequalities in C*-module

Filomat, 2014

We obtain a Generalized of Selberg's type inequalities in Hilbert spaces and their extensions in operators algebras, in C * -modules and in algebras of adjointable A-linear maps. Some applications for improving the Bessel type inequality result are given.

Operator inequalities related to the Corach–Porta–Recht inequality

Linear Algebra and its Applications, 2011

We prove some refinements of an inequality due to X. Zhan in an arbitrary complex Hilbert space by using some results on the Heinz inequality. We present several related inequalities as well as new variants of the Corach–Porta–Recht inequality. We also ...

Loading...

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.