Two Mappings Related To Semi-Inner Products And Their Applications in Geometry of Normed Linear Spaces

In this paper we introduce two mappings associated with the lower and upper semiinner product (.,.)i and (.,.)s and with semi-inner products [.,.] (in the sense of Lumer) which generate the norm of a real normed linear space, and study properties of monotonicity and boundedness of these mappings. We give a refinement of the Schwarz inequality, applications to the Birkhoff orthogonality, to smoothness of normed linear spaces as well as to the characterization of best approximants

Power bounded and exponentially bounded matrices

summary:The paper gives a new characterization of eigenprojections, which is then used to obtain a spectral decomposition for the power bounded and exponentially bounded matrices. The applications include series and integral representations of the Drazin inverse, and investigation of the asymptotic behaviour of the solutions of singular and singularly perturbed differential equations. An example is given of localized travelling waves for a system of conservation laws

Elements of rings with equal spectral idempotents

In this paper we define and study a generalized Drazin inverse $x^D$ for ring elements $x$, and give a characterization of elements $a, b$ for which $aa^D = bb^D$. We apply our results to the study of EP elements of a ring with involution.Fundação para a Ciência e a Tecnologia (FCT) - Programa Operacional "Ciência, Tecnologia, Inovação" (POCTI)

The weighted g–Drazin inverse for operators,

Abstract The paper introduces and studies th

Opial type L

This paper presents a class of Lp-type Opial inequalities for generalized fractional derivatives for integrable functions based on the results obtained earlier by the first author for continuous functions (1998). The novelty of our approach is the use of the index law for fractional derivatives in lieu of Taylor's formula, which enables us to relax restrictions on the orders of fractional derivatives

The one-sided inverse along an element in semigroups and rings

The concept of the inverse along an element was introduced by Mary in 2011. Later, Zhu et al. introduced the one-sided inverse along an element. In this paper, we first give a new existence criterion for the one-sided inverse along a product and characterize the existence of Moore–Penrose inverse by means of one-sided invertibility of certain element in a ring. In addition, we show that a∈ S † ⋂ S # if and only if (a∗a)k is invertible along a if and only if (aa∗)k is invertible along a in a ∗ -monoid S, where k is an arbitrary given positive integer. Finally, we prove that the inverse of a along aa ∗ coincides with the core inverse of a under the condition a∈ S { 1 , 4 } in a ∗ -monoid S.FCT - Fuel Cell Technologies Program(CXLX13-072)This research was supported by the National Natural Science Foundation of China (No. 11371089), the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20120092110020), the Natural Science Foundation of Jiangsu Province (No. BK20141327) and the Foundation of Graduate Innovation Program of Jiangsu Province (No. KYZZ15-0049).info:eu-repo/semantics/publishedVersio

On Inequalities in Normed Linear Spaces and Applications

In this paper we obtain inequalities involving the norms of finite sequences of vectors in normed linear spaces, which are new even for complex numbers

Spectral sets

The paper studies spectral sets of elements of Banach algebras as the zeros of holomorphic functions and describes them in terms of existence of idempotents. A new decomposition theorem characterizing spectral sets is obtained for bounded linear operators