Means of Positive Linear Operators.
Means of positive matrices: geometry and a conjecture.
Means of vector-valued functions and projections which commute with the action of a group
Mean-value theorems and ergodicity of certain geodesic random walks
Measurability of linear operators in the Skorokhod topology.
Measurable linear operators on Banach spaces
Measure of noncompactness of linear operators between spaces of sequences that are summable or bounded
In this paper we investigate linear operators between arbitrary BK spaces and spaces of sequences that are summable or bounded. We give necessary and sufficient conditions for infinite matrices to map into . Further, the Hausdorff measure of noncompactness is applied to give necessary and sufficient conditions for to be a compact operator.
Measure of noncompactness of operators and matrices on the spaces and .
Measure of non-compactness of operators interpolated by the real method
We study the measure of non-compactness of operators between abstract real interpolation spaces. We prove an estimate of this measure, depending on the fundamental function of the space. An application to the spectral theory of linear operators is presented.
Measure of noncompactness of subsets of Lebesgue spaces
Measure of nonhyperconvexity and fixed-point theorems.
Measure of weak noncompactness under complex interpolation
Logarithmic convexity of a measure of weak noncompactness for bounded linear operators under Calderón’s complex interpolation is proved. This is a quantitative version for weakly noncompact operators of the following: if T: A₀ → B₀ or T: A₁ → B₁ is weakly compact, then so is for all 0 < θ < 1, where and are interpolation spaces with respect to the pairs (A₀,A₁) and (B₀,B₁). Some formulae for this measure and relations to other quantities measuring weak noncompactness are established.
Measure theory in noncommutative spaces.
Measure-geometric Laplacians for partially atomic measures
Motivated by the fundamental theorem of calculus, and based on the works of W. Feller as well as M. Kac and M. G. Kreĭn, given an atomless Borel probability measure supported on a compact subset of U. Freiberg and M. Zähle introduced a measure-geometric approach to define a first order differential operator and a second order differential operator , with respect to . We generalize this approach to measures of the form , where is non-atomic and is finitely supported. We determine analytic...
Measures of finite (r,p)-energy and potentials on a separable metric space
Measures of noncircularity and fixed points of contractive multifunctions.
Measures of noncompactness and normal structure in Banach spaces
Sufficient conditions for normal structure of a Banach space are given. One of them implies reflexivity for Banach spaces with an unconditional basis, and also for Banach lattices.
Measures of noncompactness in Banach sequence spaces
Measures of noncompactness in locally convex spaces and fixed point theory for the sum of two operators on unbounded convex sets
In this paper we prove a collection of new fixed point theorems for operators of the form on an unbounded closed convex subset of a Hausdorff topological vector space . We also introduce the concept of demi--compact operator and -semi-closed operator at the origin. Moreover, a series of new fixed point theorems of Krasnosel’skii type is proved for the sum of two operators, where is -sequentially continuous and -compact while is -sequentially continuous (and -condensing, -nonexpansive...
Measures of non-compactness in Orlicz modular spaces.
In this paper we show that the ball-measure of non-compactness of a norm bounded subset of an Orlicz modular space L-Psi is equal to the limit of its n-widths. We also obtain several inequalities between the measures of non-compactness and the limit of the n-widths for modular bounded subsets of L-Psi which do not have Delta-2-condition. Minimum conditions on Psi to have such results are specified and an example of such a function Psi is provided.