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In this paper, we consider thequadratic weighted geometric mean for bounded linear operatorsT, Vin the Hilbert spaceHwithTinvertible and. Using the celebrated McCarthy’s inequality we show that for anywherep, withWe also provide some norm inequalities such as for anyn-tuples of invertible operatorsand anyn-tuple of positive weights. [ABSTRACT FROM PUBLISHER]

A Buzano type inequality for two nonnegative Hermitian forms is obtained. Applications to inequalities for norm and numerical radius of bounded linear operators in complex Hilbert spaces are given. [ABSTRACT FROM AUTHOR]

In this paper, some new inequalities for power series via Buzano's result are obtained. Applications for some fundamental complex functions are also provided. [ABSTRACT FROM AUTHOR]

Some inequalities for continuous functions of selfadjoint operators in Hilbert spaces that improve the Cauchy-Bunyakovsky-Schwarz inequality, are given. [ABSTRACT FROM AUTHOR]

Regarding the generalizations of the Bessel inequality in Hilbert spaces which are due to Bombieri and Boas-Bellman, we obtain a version of the Bessel inequality and some generalizations of this inequality in the framework of Hilbert C *-modules. [ABSTRACT FROM AUTHOR]

Some inequalities for continuous synchronous (asynchronous) functions of selfadjoint linear operators in Hilbert spaces, under suitable assumptions for the involved operators, are given. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some operator inequalities for functions defined by power series with real coefficients and, more specifically, with nonnegative coefficients. In order to obtain these inequalities, some recent reverses of the Schwarz inequality for vectors in inner product spaces are utilized. Natural applications for some elementary functions of interest are also provided. [ABSTRACT FROM AUTHOR]

Some inequalities for power series with real coefficients via the de Bruijn inequality are established. Applications for fundamental complex functions such as the exp, cos, sin, cosh, sinh and ln are also given. [ABSTRACT FROM AUTHOR]

Let q » 1 be a fixed integer number. We prove that a discrete q-periodic evolution family U = {U(m, n) : (m, n) ϵ Z+ ⊗ Z+, m ≥ n ≥ 0} on a complex Banach space X is uniformly asymptotically stable, that is, U(m, n) ↵ 0 in the norm of L(X) when (m - n) ↵ ∞, if and only if for each μ ϵ R and each x ϵ X one has [This symbol cannot be presented in ASCII format]. In particular, we obtain the following result of Datko type. The family U is uniformly asymptotically stable if and only if for each x ϵ X one has [This symbol cannot be presented in ASCII format]. [ABSTRACT FROM AUTHOR]