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• # Artykuł - szczegóły

## Studia Mathematica

2010 | 196 | 1 | 23-40

## Biseparating maps on generalized Lipschitz spaces

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.

23-40

wydano
2010

### Twórcy

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