In this note, we will discuss how to relate an operator ideal on Banach spaces to the sequential structures it defines. Concrete examples of ideals of compact, weakly compact, completely continuous, Banach-Saks and weakly Banach-Saks operators will be demonstrated.

Let V,W∞, andW be operator ideals of completely continuous, weakly ∞-compact, and weakly compact operators, respectively. We prove that V =W∞ ◦W−1. As an immediate application, the recent result by Dowling, Freeman, Lennard, Odell, Randrianantoanina, and Turett follows: the weak Grothendieck compactness principle holds only in Schur spaces.

We present some improvements in the method of the weakly conjugate operator, one variant of the Mourre theory. When applied to certain two-body Schrödinger operators, this leads to a limiting absorption principle that is uniform on the positive real axis. Mathematics Subject Classification (2000): 35P05, 46L60, 47A10, 81Q10.

We consider spectral radius algebras associated to C0 contractions. When the operator A is algebraic, we describe all invariant subspaces that are common for operators in its spectral radius algebra BA. In all other situations BA is weakly dense and we characterize a set of rank one operators in BA that is weakly dense in L(H).

Kinetic eigenmodes of plasma oscillations in a weakly collisional plasma, described by a collision operator of the Fokker-Planck type, are obtained in closed form for initial-value as well as for boundary-value problems. These eigenmodes, which are smooth and compose a complete discrete spectrum, play the same role for weakly collisional plasmas as the Case-Van Kampen modes do for collisionless...

A theorem of Davis, Figiel, Johnson and Pe lczyński tells us that weakly-compact operators between Banach spaces factor through reflexive Banach spaces. The machinery underlying this result is that of the real interpolation method, which has been adapted to the category of operator spaces by Xu, showing the this factorisation result also holds for completely bounded weakly-compact maps. In this...

We consider maps of the family of convex bodies in Euclidean ddimensional space into itself that are compatible with certain structures on this family: A Minkowski-endomorphism is a continuous, Minkowski-additive map that commutes with rotations. For d ≥ 3, a representation theorem for such maps is given, showing that they are mixtures of certain prototypes. These prototypes are obtained by app...

Abstract In this study, an initial-value problem for a nonlinear Volterra functional integro-differential equation on finite interval was considered. The term in the contains multiple time delays. addition to giving some new theorems existence and uniqueness of solutions equation, authors also prove Hyers-Ulam-Rassias stability Hyers-Ulam equation. proofs use several different tools including B...

The investigation of the foundational aspects of linguistic mechanisms for programming long running transactions (such as the scope operator of WS-BPEL) has recently renewed the interest in process algebraic operators that interrupt the execution of one process, replacing it with another one called the compensation. We investigate the expressive power of two of such operators, the interrupt ope...

This paper introduce a iteration scheme for approximation of strongly accretive operator equations in reflexive Banach space with weakly continuous duality mapping. Our result improve the results of Y. Xu [Ishikawa and Mann Iterative Processes with Errors for Nonlinear Strongly Accretive Operator Equations, J. Math. Anal Appl. 224(1998) 91-101] and I. Inchan and S. Plubtieng [Approximating solu...