An extension of a theorem of Rosenthal on operators acting from
An extension of a theorem of Sahab, Khan, and Sessa.
An extension of Amir-Lindenstrauss theorem.
An extension of Choquet boundary theory to certain partially ordered compact convex sets
An extension of distributional wavelet transform
We construct a new Boehmian space containing the space 𝓢̃'(ℝⁿ×ℝ₊) and define the extended wavelet transform 𝓦 of a new Boehmian as a tempered Boehmian. In analogy to the distributional wavelet transform, it is proved that the extended wavelet transform is linear, one-to-one, and continuous with respect to δ-convergence as well as Δ-convergence.
An extension of Duhamel's integral to differential equations involving generalized functions; the steady-state solution
An extension of Helly's theorem for Banach spaces
An extension of Helson-Edwards theorem to Banach modules.
An extension of Lorentz's almost convergence and applications in Banach spaces
2000 Mathematics Subject Classification: Primary 40C99, 46B99.We investigate an extension of the almost convergence of G. G. Lorentz requiring that the means of a bounded sequence converge uniformly on a subset M of N. We also present examples of sequences α∈ l∞(N) whose sequences of translates (Tn α)n≥ 0 (where T is the left-shift operator on l∞(N)) satisfy: (a) Tn α, n ≥ 0 generates a subspace E(α) of l∞(N) that is isomorphically embedded into c0 while α is not almost convergent. (b) Tn...
An extension of Mazur's theorem on Gateaux differentiability to the class of strongly α (·)-paraconvex functions
Let (X,||·||) be a separable real Banach space. Let f be a real-valued strongly α(·)-paraconvex function defined on an open convex subset Ω ⊂ X, i.e. such that . Then there is a dense -set such that f is Gateaux differentiable at every point of .
An Extension of Milman's Reverse Brunn-Minkowski Inequality.
An extension of Simons' inequality and applications.
This article is devoted to an extension of Simons' inequality. As a consequence, having a pointwise converging sequence of functions, we get criteria of uniform convergence of an associated sequence of functions.
An extension of the inverse function theorem.
An extension of the Krein-Smulian theorem.
Let X be a Banach space, u ∈ X** and K, Z two subsets of X**. Denote by d(u,Z) and d(K,Z) the distances to Z from the point u and from the subset K respectively. The Krein-Smulian Theorem asserts that the closed convex hull of a weakly compact subset of a Banach space is weakly compact; in other words, every w*-compact subset K ⊂ X** such that d(K,X) = 0 satisfies d(cow*(K),X) = 0.We extend this result in the following way: if Z ⊂ X is a closed subspace of X and K ⊂ X** is a w*-compact subset of...
An extension of Whitney's spectral theorem
An extension of Witzgall's result on convex metrics.
An extension property for Banach spaces
A Banach space X has property (E) if every operator from X into c₀ extends to an operator from X** into c₀; X has property (L) if whenever K ⊆ X is limited in X**, then K is limited in X; X has property (G) if whenever K ⊆ X is Grothendieck in X**, then K is Grothendieck in X. In all of these, we consider X as canonically embedded in X**. We study these properties in connection with other geometric properties, such as the Phillips properties, the Gelfand-Phillips and weak Gelfand-Phillips properties,...
An extension theorem of functionals on commutative semigroups
An extension theorem to rough paths
An extremal problem in Banach algebras
We study asymptotics of a class of extremal problems rₙ(A,ε) related to norm controlled inversion in Banach algebras. In a general setting we prove estimates that can be considered as quantitative refinements of a theorem of Jan-Erik Björk [1]. In the last section we specialize further and consider a class of analytic Beurling algebras. In particular, a question raised by Jan-Erik Björk in [1] is answered in the negative.