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Extenders for vector-valued functions

Iryna Banakh, Taras Banakh, Kaori Yamazaki (2009)

Studia Mathematica

Given a subset A of a topological space X, a locally convex space Y, and a family ℂ of subsets of Y we study the problem of the existence of a linear ℂ-extender u : C ∞ ( A , Y ) → C ∞ ( X , Y ) , which is a linear operator extending bounded continuous functions f: A → C ⊂ Y, C ∈ ℂ, to bounded continuous functions f̅ = u(f): X → C ⊂ Y. Two necessary conditions for the existence of such an extender are found in terms of a topological game, which is a modification of the classical strong Choquet game. The results obtained allow us...

Extension of vector-valued holomorphic and harmonic functions

José Bonet, Leonhard Frerick, Enrique Jordá (2007)

Studia Mathematica

We present a unified approach to the study of extensions of vector-valued holomorphic or harmonic functions based on the existence of weak or weak*-holomorphic or harmonic extensions. Several recent results due to Arendt, Nikolski, Bierstedt, Holtmanns and Grosse-Erdmann are extended. An open problem by Grosse-Erdmann is solved in the negative. Using the extension results we prove existence of Wolff type representations for the duals of certain function spaces.

Extensions of the representation theorems of Riesz and Fréchet

João C. Prandini (1993)

Mathematica Bohemica

We present two types of representation theorems: one for linear continuous operators on space of Banach valued regulated functions of several real variables and the other for bilinear continuous operators on cartesian products of spaces of regulated functions of a real variable taking values on Banach spaces. We use generalizations of the notions of functions of bounded variation in the sense of Vitali and Fréchet and the Riemann-Stieltjes-Dushnik or interior integral. A few applications using geometry...

Factorization of Montel operators

S. Dierolf, P. Domański (1993)

Studia Mathematica

Consider the following conditions. (a) Every regular LB-space is complete; (b) if an operator T between complete LB-spaces maps bounded sets into relatively compact sets, then T factorizes through a Montel LB-space; (c) for every complete LB-space E the space C (βℕ, E) is bornological. We show that (a) ⇒ (b) ⇒ (c). Moreover, we show that if E is Montel, then (c) holds. An example of an LB-space E with a strictly increasing transfinite sequence of its Mackey derivatives is given.

Factorization of operators on C*-algebras

Narcisse Randrianantoanina (1998)

Studia Mathematica

Let A be a C*-algebra. We prove that every absolutely summing operator from A into ℓ 2 factors through a Hilbert space operator that belongs to the 4-Schatten-von Neumann class. We also provide finite-dimensional examples that show that one cannot replace the 4-Schatten-von Neumann class by the p-Schatten-von Neumann class for any p < 4. As an application, we show that there exists a modulus of capacity ε → N(ε) so that if A is a C*-algebra and T ∈ Π 1 ( A , ℓ 2 ) with π 1 ( T ) ≤ 1 , then for every ε >0, the ε-capacity of...

Currently displaying 121 – 140 of 427