Given an infinite-dimensional Banach space X, we introduce the daugavetian index of X , daug (X), as the greatest constant m > 0 such that kId+ Tk > 1 +mkTk for all T ∈ K(X). We givetwo characterizations of this index and we estimate it in some examples. We show that the daugavetian index of a c0-, l1or l∞-sum of Banach spaces is the infimum index of the summands. Finally, we calculate the daug...

Let V be an arbitrary system of weights on an open connected subset G of CN (N ≥ 1) and let B(E) be the Banach algebra of all bounded linear operators on a Banach space E. LetHVb (G,E) andHV0 (G,E) be the weighted locally convex spaces of vector-valued analytic functions. In this survey, we present a development of the theory of multiplication operators and composition operators from classical ...

Most of the results for laws of large numbers based on Banach space valued random sets assume that the sets are independent and identically distributed (IID), and compact, in which R̊adström embedding or the refined method for collection of compact and convex subsets of a Banach space plays an important role. In this paper, exchangeability among random sets as a dependency, instead of IID, is as...

This article deals with a vector optimization problem with cone constraints in a Banach space setting. By making use of a real-valued Lagrangian and the concept of generalized subconvex-like functions, weakly efficient solutions are characterized through saddle point type conditions. The results, jointly with the notion of generalized Hessian (introduced in [Cominetti, R., Correa, R.: A general...

We precede the proof with some necessary definitions and notation. Two Banach lattices X and Y are said to be order isometric if there exists an isometry U of X onto Y which preserves the order, that is, U is an isometric surjective operator and U(x) ≥ 0 if and only if x ≥ 0. Let L0 = L0[0, 1] be the vector lattice of all (equivalence classes of) measurable real valued functions on [0, 1] and l...

Let Q ? R m , K n be open sets, p q ? N 1 ? r < ? and let E F Banach spaces. Denote by C ? ( ) the space of all f with bounded derivatives order endowed norm ? = sup s ? [ ? ? ? ] where ? denotes ? on { : | } . T ? a linear surjective isometry. Then there are -diffeomorphism ? isomorphisms V t so that if The result holds in more general setting. proof establishes direct link between isometries ...

Let X,Y, Z be Banach spaces and let u : X×Y → Z be a bounded bilinear map. Given a locally compact abelian group G , and two functions f ∈ L(G,X) and g ∈ L(G,Y ), we define the u -convolution of f and g as the Z -valued function f ∗u g(t) = ∫ G u(f(t− s), g(s))dμG(s) where dμG stands for the Haar measure on G . We define the concepts of vector-valued approximate identity and summability kernel ...

Abstract: Let m : Σ → X be a Banach space valued countably additive vector measure. In this paper we present a procedure to construct an m -orthogonal system in the space L(m) of square integrable functions with respect to m . If the vector measure is constructed from a family of indeterminate scalar measures, it is possible to obtain a family of polynomials that is orthogonal with respect to t...

We consider metric measure spaces satisfing a doubling condition and a Poincaré inequality in the upper gradient sense. We show that the results of [Che99] on differentiability of real valued Lipschitz functions and the resulting bi-Lipschitz nonembedding theorems for finite dimensional vector space targets extend to Banach space targets having what we term a good finite dimensional approximati...