On reflexive spaces trigonometrically well-bounded operators (abbreviated “twbo’s”) have an operator-ergodic-theory characterization as the invertible operators U whose rotates “transfer” the discrete Hilbert averages (C, 1)-boundedly. Twbo’s permeate many settings of modern analysis, and this note treats advances in their spectral theory, Fourier analysis, and operator ergodic theory made poss...

Let $X$ be a reflexive Banach space, $T:Xto X$ be a nonexpansive mapping with $C=Fix(T)neqemptyset$ and $F:Xto X$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. In this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences ...

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...

This work introduces the concept of an M-complete approximate identity (M-cai) for a given operator subspace X of an operator space Y. M-cai's generalize central approximate identities in ideals in C *-algebras, for it is proved that if X admits an M-cai in Y , then X is a complete M-ideal in Y. It is proved, using " special " M-cai's, that if J is a nuclear ideal in a C *-algebra A, then J is ...

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...