In this paper we study some properties of the classical Arnoldi based methods for solving infinite dimensional linear equations involving compact operators. These problems are intrinsically ill-posed since a compact operator does not admit a bounded inverse. We study the convergence properties and the ability of these algorithms to estimate the dominant singular values of the operator.

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

In this work we provide a characterization of distinct types (linear and non-linear) maps between Banach spaces in terms the differentiability certain class Lipschitz functions. Our results are stated an abstract bornological non-linear framework. Restricted to linear case, can apply our compact, weakly-compact, limited completely continuous operators. Moreover, yield Gelfand-Phillips recover s...

A bounded linear operator between Banach spaces is called completely continuous if it carries weakly convergent sequences into norm convergent sequences. Isolated is a universal operator for the class of non-completely-continuous operators from L1 into an arbitrary Banach space, namely, the operator from L1 into l∞ defined by

The discretization of the viscous operator in an edge-based flow solver for unstructured grids has been investigated. A compact discretization of the Laplace and thin-layer operators in the viscous terms is used with two different wall boundary conditions. Furthermore, a wide discretization of the same operators is investigated. The resulting numerical operators are all formally second order ac...

Let $(X,d)$ be an infinite compact metric space, let $(B,parallel . parallel)$ be a unital Banach space, and take $alpha in (0,1).$ In this work, at first we define the big and little $alpha$-Lipschitz vector-valued (B-valued) operator algebras, and consider the little $alpha$-lipschitz $B$-valued operator algebra, $lip_{alpha}(X,B)$. Then we characterize its second dual space.

The famous Lomonosov’s invariant subspace theorem states that if a continuous linear operator T on an infinite-dimensional normed space E “commutes” with a compact operator K 6= 0, i.e., TK = KT, then T has a non-trivial closed invariant subspace. We generalize this theorem for multivalued linear operators. We also provide some applications to singlevalued linear operators.

We prove that the class of Banach function lattices in which all relatively weakly compact sets are equi-integrable (i.e. spaces satisfying Dunford–Pettis criterion) coincides with 1-disjointly homogeneous lattices. New examples such provided. Furthermore, it is shown criterion equivalent to de la Valleé Poussin rearrangement invariant on interval. Finally, results applied characterize pointwis...