We determine the computational complexity of the Hahn-Banach Extension Theorem. To do so, we investigate some basic connections between reverse mathematics and computable analysis. In particular, we use Weak König’s Lemma within the framework of computable analysis to classify incomputable functions of low complexity. By defining the multi-valued function Sep and a natural notion of reducibilit...

Let X be a Banach space and (Ω,Σ) be a measure space. We provide a characterization of sequences in the space of X-valued countably additive measures on (Ω,Σ) of bounded variation that generates complemented copies of l1. As application, we prove that if a dual Banach space E∗ has Pe lczyński’s property (V*) then so does the space of E∗-valued countably additive measures with the variation norm...

Let K be a (commutative) locally compact hypergroup with a left Haar measure. Let L1(K) be the hypergroup algebra of K and UCl(K) be the Banach space of bounded left uniformly continuous complex-valued functions on K. In this paper we show, among other things, that the topological (algebraic) center of the Banach algebra UCl(K)* is M(K), the measure algebra of K.

A two-phase two-component model is formulated for the advective-diffusive transport of methane in liquid phase through sediment with the accompanying formation and dissolution of methane hydrate. This free-boundary problem has a unique generalized solution in L; the proof combines analysis of the stationary semilinear elliptic Dirichlet problem with the nonlinear semigroup theory in Banach spac...

It is not known a satisfactory way to compute adjoints of composition operators, yet in classical functional Banach spaces (cf. [3]). If K is the reproducing kernel of a functional Hilbert space H, g ∈ H and the composition operator Cφ is bounded then C∗ φg (z) = 〈g(t),K (z, φ (t))〉H , z ∈ D. In general, although reproducing kernels might be described in series developments, it is not possible ...

We consider Fourier series of functions in L(0, 2π;X) where X is a Banach space. In particular, we show that the Fourier series of each function in L(0, 2π;X) converges unconditionally if and only if p = 2 and X is a Hilbert space. For operator-valued multipliers we present the Marcinkiewicz theorem and give applications to differential equations. In particular, we characterize maximal regulari...

The Lipschitz function algebras were first defined in the 1960s by some mathematicians, including Schubert. Initially, the Lipschitz real-value and complex-value functions are defined and quantitative properties of these algebras are investigated. Over time these algebras have been studied and generalized by many mathematicians such as Cao, Zhang, Xu, Weaver, and others. Let  be a non-emp...

In this paper we prove a central limit theorem for Borel measurable nonseparably valued random elements in the case of Banach space valued fuzzy random variables.