Biseparating maps on generalized Lipschitz spaces

• Autorzy: Denny H. Leung
• Języki publikacji: EN

Abstrakty

EN

Let X, Y be complete metric spaces and E, F be Banach spaces. A bijective linear operator from a space of E-valued functions on X to a space of F-valued functions on Y is said to be biseparating if f and g are disjoint if and only if Tf and Tg are disjoint. We introduce the class of generalized Lipschitz spaces, which includes as special cases the classes of Lipschitz, little Lipschitz and uniformly continuous functions. Linear biseparating maps between generalized Lipschitz spaces are characterized as weighted composition operators, i.e., of the form $Tf(y) = S_{y}(f(h^{-1}(y)))$ for a family of vector space isomorphisms $S_{y}: E → F$ and a homeomorphism h: X → Y. We also investigate the continuity of T and related questions. Here the functions involved (as well as the metric spaces X and Y) may be unbounded. Also, the arguments do not require the use of compactification of the spaces X and Y.

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 47B38: Operators on function spaces (general)
• 47B33: Composition operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 196
• Numer: 1
• Strony: 23-40

Daty

wydano

2010

Twórcy

autor

Denny H. Leung

• Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543

Identyfikatory

DOI

10.4064/sm196-1-3