Fredholm radius of a potential theoretic operator for convex sets

On a convex operator for finite sets

Let S be a finite set with n elements in a real linear space. Let JS be a set of n intervals in R. We introduce a convex operator co(S,JS) which generalizes the familiar concepts of the convex hull conv S and the affine hull aff S of S. We establish basic properties of this operator. It is proved that each homothet of conv S that is contained in aff S can be obtained using this operator. A vari...

Fuzzy sets form A meta-system-theoretic point of view

The image of a closed convex set under a Fredholm operator

The purpose of this article is two-fold. In the first place, we prove that a set is the image of a non empty closed convex subset of a real Banach space under an onto Fredholm operator of positive index if and only if it can be written as the union of {Dn : n ∈ N}, a non-decreasing family of non empty, closed, convex and bounded sets such that Dn + Dn+2 ⊆ 2Dn+1 for every n ∈ N. The second part ...

Egoroff Theorem for Operator-Valued Measures in Locally Convex Cones

In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...

The Stability Radius of Fredholm Linear Pencils

Let T and S be two bounded linear operators from Banach spaces X into Y and suppose that T is Fredholm and dimN(T − λS) is constant in a neighborhood of λ = 0. Let d(T ;S) be the supremum of all r > 0 such that dimN(T − λS) and codim R(T − λS) are constant for all λ with |λ| < r. It is a consequence of more general results due to H. Bart and D.C. Lay (1980) that d(T ;S) = limn→∞ γn(T ;S) , wher...