Abstract The purpose of this paper is to present in linear spaces some results for new notions called A -left (resp., -right) ascent and descent operators (where a given operator) which generalize two important operator theory: descent. Moreover, if positive operator, we obtain several properties an semi-Hilbertian spaces. Some basic many related the on space Kaashoek (Math Ann 172:105–115, 196...

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 ...

Throughout this paper X denotes a bicompact space, B(X) denotes the Banach space of all bounded real-valued functions on X, C(X) denotes the closed linear subspace of B(X) of continuous real-valued functions on X, B(N) is denoted by m (where N is the set of positive integers). The space h(X) is the Banach space of all absolutely summable real-valued functions on X and k denotes k(N). The sequen...

Assuming Jensen's diamond principle (⋄) we construct for every natural number n>0 a compact Hausdorff space K such that whenever the Banach spaces C(K) and C(L) are isomorphic some L, then covering dimension of L is equal to n. The constructed separable connected, has few operators i.e. bounded linear operator T:C(K)→C(K) form T(f)=fg+S(f), where g∈C(K) S weakly compact.

Toeplitz operators are fundamental and ubiquitous in signal processing and information theory as models for linear, time-invariant (LTI) systems. Due to the fact that any practical system can access only signals of finite duration, time-limited restrictions of Toeplitz operators are naturally of interest. To provide a unifying treatment of such systems working on different signal domains, we co...

A Banach space E has the Grothendieck property if every (linear bounded) operator from E into c0 is weakly compact. It is proved that, for an integer k > 1, every k-homogeneous polynomial from E into c0 is weakly compact if and only if the space P(kE) of scalar valued polynomials on E is reflexive. This is equivalent to the symmetric k-fold projective tensor product of E (i.e., the predual of P...

Ahsfract-Using the notion of fading memory we prove very strong versions of two folk theorems. The first is that any time-inuariant (TZ) con~inuou.r nonlinear operator can be approximated by a Volterra series operator, and the second is that the approximating operator can be realized as a finiiedimensional linear dynamical system with a nonlinear readout map. While previous approximation result...

In this note we will present an extension of the Krein-Rutman theorem for an abstract non-linear, compact, positively 1-homogeneous operators on a Banach space having the properties of being increasing with respect to a convex cone K and such that there is a non-zero u ∈ K for which M Tu < u for some positive constant M . This will provide a uniform framework for recovering the Krein-Rutman-lik...

Let (M, g) be a Riemannian surface (i.e. a Riemannian manifold of dimension 2), orientable or not. We assume that M is either compact or a compact perturbation of the euclidian space, so that the Sobolev embeddings are true. Consider ∆ = ∆ g the Laplace-Beltrami operator. In this paper we are interested in constructing WKB approximations for the non linear cubic Schrödinger equation i∂ t u(t, x...