In this paper, we study an iterative scheme for two different types of resolvents of a monotone operator defined on a Banach space. These resolvents are generalizations of resolvents of a monotone operator in a Hilbert space. We obtain iterative approximations of a zero point of a monotone operator generated by the shrinking projection method with errors in a Banach space. Using our result, we ...

Let X be a Banach space and T be a bounded linear operator from X to itself (T ∈ B(X).) An operator S ∈ B(X) is a generalized inverse of T if TST = T . In this paper we look at several Banach algebras of operators and characterize when an operator in that algebra has a generalized inverse that is also in the algebra. Also, Drazin inverses will be related to generalized inverses and spectral pro...

We prove that each positive operator from a Banach lattice E to a Banach lattice F with a disjointly strictly singular majorant is itself disjointly strictly singular provided the norm on F is order continuous. We prove as well that if S : E → E is dominated by a disjointly strictly singular operator, then S2 is disjointly strictly singular.

Abstract. Here a new condition for the geometry of Banach spaces is introduced and the operator–valued Fourier multiplier theorems in weighted Besov spaces are obtained. Particularly, connections between the geometry of Banach spaces and Hörmander-Mikhlin conditions are established. As an application of main results the regularity properties of degenerate elliptic differential operator equation...

In this paper, we study the properties of the metric projection operator (the nearest point projection operator) and its continuity. Then we use it to solve variational inequalities in general Banach spaces and to approximate the solutions in uniformly convex and uniformly smooth Banach spaces.

We show that every free semigroup algebras has a (strongly) unique Banach space predual. We also provide a new simpler proof that a weak-∗ closed unital operator operator algebra containing a weak-∗ dense subalgebra of compact operators has a unique Banach space predual.

‎Let $mathcal{A}$ be a commutative Banach algebra and $mathscr{X}$ be a left Banach $mathcal{A}$-module‎. ‎We study the set‎ ‎${rm Dec}_{mathcal{A}}(mathscr{X})$ of all elements in $mathcal{A}$ which induce a decomposable multiplication operator on $mathscr{X}$‎. ‎In the case $mathscr{X}=mathcal{A}$‎, ‎${rm Dec}_{mathcal{A}}(mathcal{A})$ is the well-known Apostol algebra of $mathcal{A}$‎. ‎We s...

Let $T$ be a bounded operator on the Banach space $X$ and $ph$ be an analytic self-map of the unit disk $Bbb{D}$‎. ‎We investigate some operator theoretic properties of‎ ‎bilateral composition operator $C_{ph‎, ‎T}‎: ‎f ri T circ f circ ph$ on the vector-valued Hardy space $H^p(X)$ for $1 leq p leq‎ ‎+infty$.‎ ‎Compactness and weak compactness of $C_{ph‎, ‎T}$ on $H^p(X)$‎ ‎are characterized an...

in this article we study two different generalizations of von neumann regularity, namely strong topological regularity and weak regularity, in the banach algebra context. we show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. then we consider strong topological regularity of certain concrete algebras. moreover we obtain ...