This paper deals with the so-called A-numerical radius associated a positive (semi-definite) bounded linear operator A acting on complex Hilbert space H. Several new inequalities involving this concept are established. In particular, we prove several estimates for 2×2 matrices whose entries A-bounded operators. Some of obtained results cover and extend well-known recent due to Bani-Domi Kittane...

In this work, the gap between operator norm and spectral radius for square of antidiagonal block matrices in direct sum Banach spaces has been investigated, also numerical same Hilbert studied.

Several refinements of norm and numerical radius inequalities bounded linear operators on a complex Hilbert space are given. In particular, we show that if A is operator space, then 14A*A+AA*≤18A+A*2+A−A*2+c2(A+A*)+c2(A−A*)≤w2(A) 12A∗A+AA∗−14(A+A∗)2(A−A∗)212≤w2(A)≤12A∗A+AA∗, where ∥⋅∥, w(⋅) c(⋅) the norm, Crawford number, respectively. Further, prove A, D AD∗≤∫01(1−t)(A2+D2)/2+tAD∗I2dt12≤12A2+D...

The main aim of the present paper is to establish some norm and numerical radius inequalities for the composite operator BA under suitable assumptions for the transform Cα,β (T ) := (T ∗ −αI) (β I−T ) , where α ,β ∈ C and T ∈ B(H), of the operators involved. Mathematics subject classification (2000): Primary 47A12, 47A30; Secondary 47A63..

In this work, some generalized Euclidean operator radius inequalities are established. Refinements of well-known results provided. Among others, bounds in terms the Cartesian decomposition a given Hilbert space proven.

let a be a bounded linear operator on a banach space x. we investigate the conditions of existing rank-one operator b such that i+f(a)b is invertible for every analytic function f on sigma(a). also we compare the invariant subspaces of f(a)b and b. this work is motivated by an operator method on the banach space ell^2 for solving some pdes which is extended to general operator space under some ...

We determine the L spectrum of the Laplace-Beltrami operator on certain complete locally symmetric spaces M whose universal covering X is a symmetric space of non-compact type with rank one. More precisely, we show that the L spectra of M and X coincide if the fundamental group of M is small and if the injectivity radius of M is bounded away from zero. In the L case, the restriction on the inje...

We prove new inequalities for the spectral radius, essential operator norm, measure of noncompactness and numerical radius Hadamard weighted geometric means positive kernel operators on Banach function sequence spaces. Some extend refine known that have been established by several authors relatively recently. Several appear to be even in finite dimensional case.

In this paper the theory of evolution semigroups is developed and used to provide a framework to study the stability of general linear control systems. These include autonomous and nonautonomous systems modeled with unbounded state-space operators acting on Banach spaces. This approach allows one to apply the classical theory of strongly continuous semigroups to timevarying systems. In particul...