Then T is compact on Aαp(B) if and only if T fk → 0 in Aαp(B) for any bounded sequence { fk} in Aαp(B) such that fk → 0 uniformly on compact subsets of B. A proof can be found in [3, Proposition 3.11] for a single composition operator and it can be easily ...
P.L茅vy considered the upper and lower class with regard to the uniform continuity of Brownian motion. We...doi:10.1016/0021-9045(74)90102-6M.B MarcusJournal of Approximation TheoryMarcus, M. B. (1974). The ε-entropy of some compact subsets of l p . J. Approximation Theory 10 , ...
Let P be the family of all finite subsets of A ordered by set inclusion. Let Ap be the subalgebra of A generated by p ∈ P . Since V is finitely generated, every Ap is finite. For every p, q ∈ P , p ≤ q, we put Lp = Conc Ap and ϕp,q = Conc ep,q, where ep,q...
If a space has a dense conditionally compact subset, it follows that it is pseudocompact, but the converse is not true. Examples are given of spaces that are pseudocompact, do not have dense conditionally compact subsets, but do have compactifications that are products of first countable ...
来自 ResearchGate 喜欢 0 阅读量: 714 作者: J Simon 摘要: In this paper we prove that the maximal operator where σ n k is the n-th Fejér mean of the Walsh-Kaczmarz-Fourier series, is bounded from the Hardy space H 1/2(G) to the space L1/2(G). 被引量: 777 年份: 1987 ...
≥ 0. This yields compactness properties of subsets of P SH(X, ω) (see section 1) which are quite useful (e.g. in complex dynamics, see section 6.2). ? Integration by parts (of constant use in such theories) is quite simple in the compact setting since there is no boundary. As ...
Subsets of these general sets include common fuzzy sets, such as fuzzy numbers, fuzzy star-shaped numbers with respect to the origin, fuzzy star-shaped numbers, and general fuzzy star-shaped numbers. Existing compactness criteria are stated for fuzzy numbers space, the space of fuzzy star-shaped...
Compact Convex Subsets of nThe following sections are included:Support FunctionsSteiner Centroid and ParametrizationLp-MetricsA Banach Space of Asymmetry ClassesBibliographical Notes#Support Functions#Steiner Centroid and Parametrization#Lp-Metrics#A Banach Space of Asymmetry Classes#Bibliographical Notes...
Let d the space of non-empty convex compact subsets of d (2≤d<+∞). The Hausdorff metric δ∞ on d is given by the formula δ∞ (K,L)=sup e∈S d-1 |δ * (e,K)-δ * (e,L)| where δ * (e,·) is the support functional of a non-empty convex compact set in d and...
In a recent paper it is shown that this classification can be performed by certain simple structures involving linear functionals and memoryless nonlinear elements, assuming that the Cj are compact subsets of a real normed linear space. Here we give a similar solution to the problem under the ...