Extending Lipschitz Maps into C ( K ) - Spaces

Extension of linear operators and Lipschitz maps into C(K)-spaces

We study the extension of linear operators with range in a C(K)space, comparing and contrasting our results with the corresponding results for the nonlinear problem of extending Lipschitz maps with values in a C(K)space. We give necessary and sufficient conditions on a separable Banach space X which ensure that every operator T : E → C(K) defined on a subspace may be extended to an operator e T...

Bounded Composition Operators on Holomorphic Lipschitz and Bloch Spaces of the Polydisk

Let 0 ≤ α < 1. Denote the open unit polydisk in C by ∆. We obtain a purely function-theoretic condition characterizing the holomorphic self-maps of ∆ that induce bounded composition operators on (1−α)-Bloch spaces, which we define on ∆. As a consequence, we extend Madigan’s characterization of bounded composition operators on analytic α-Lipschitz spaces over ∆ for 0 < α < 1 to an analogous char...

Extending Functions in the Model Subspaces of H^2(R) to C

Lipschitz quotients from metric trees and from Banach spaces containing l1

A Lipschitz map f between the metric spaces X and Y is called a Lipschitz quotient map if there is a C > 0 (the smallest such C, the co-Lipschitz constant, is denoted coLip(f), while Lip(f) denotes the Lipschitz constant of f) so that for every x ∈ X and r > 0, fBX(x, r) ⊃ BY (f(x), r/C). Thus Lipschitz quotient maps are surjective maps which by definition have the property ensured by the open ...

Continuous $k$-Fusion Frames in Hilbert Spaces

The study of the c$k$-fusions frames shows that the emphasis on the measure spaces introduces a new idea, although some similar properties with the discrete case are raised. Moreover, due to the nature of measure spaces, we have to use new techniques for new results. Especially, the topic of the dual of frames  which is important for frame applications, have been specified  completely for the c...