If X,Y are normed spaces, let B(X,Y ) be the set of all bounded linear maps X → Y . If T : X → Y is a linear map, I take it as known that T is bounded if and only if it is continuous if and only if E ⊆ X being bounded implies that T (E) ⊆ Y is bounded. I also take it as known that B(X,Y ) is a normed space with the operator norm, that if Y is a Banach space then B(X,Y ) is a Banach space, that ...

motivated by an arens regularity problem, we introduce the concepts of matrix banach space and matrix banach algebra. the notion of matrix normed space in the sense of ruan is a special case of our matrix normed system. a matrix banach algebra is a matrix banach space with a completely contractive multiplication. we study the structure of matrix banach spaces and matrix banach algebras. then we...

Very recently, Ahmad and Yao 2009 introduced and considered a system of generalized resolvent equationswith corresponding system of variational inclusions in uniformly smooth Banach spaces. In this paper we introduce and study a general system of generalized resolvent equations with corresponding general system of variational inclusions in uniformly smooth Banach spaces. We establish an equival...

We consider the discretization in time of a fractional order diffusion equation. The approximation is based on a further development of the approach of using Laplace transformation to represent the solution as a contour integral, evaluated to high accuracy by quadrature. This technique reduces the problem to a finite set of elliptic equations with complex coefficients, which may be solved in pa...

Consider the initial value problem ~u(t) = Au(t) + f(t), t > 0, (1.2) "(0) = "0, where A is a linear operator taking D(A) C X into X, where A" is a Banach space. Consider also semidiscrete numerical methods of the form: find UpA]t): [0, T] ■—► XN such that dUN (1.1') Sf = ANUN + PNl(1-2*) £/jv<0) = u% e xN, where X^¡ is a finite dimensional subspace and P¡y is a projector onto X^¡. The study of...

Abstract In this article, we study the controllability for impulsive fractional integro-differential evolution equation in a Banach space. The discussions are based on Mönch fixed point theorem as well theory of calculus and $(\alpha ,\beta )$ ( α , β ) ...

Abstract. Let L be an elliptic differential operator with bounded measurable coefficients, acting in Bochner spaces Lp(Rn;X) of X-valued functions on Rn. We characterize Kato’s square root estimates ‖ √ Lu‖p h ‖∇u‖p and the H-functional calculus of L in terms of R-boundedness properties of the resolvent of L, when X is a Banach function lattice with the UMD property, or a noncommutative Lp spac...

This paper is concerned with characterizations of those linear, closed, but not necessarily densely defined operators A on a Banach space E with nonempty resolvent set for which the abstract Cauchy problem u'(t) = Au(t), u(0) = x has unique, exponentially bounded solutions for every initial value x e D(A). Investigating these operators we are led to the class of "integrated semigroups". Among o...

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 ...