Zero-Set Containment and Nonvanishing Preservers of Lipschitz Functions

Lei Li ； Ya-Shu Wang

《Proceedings 10th Taiwan-Philippines Symposium on Analysis》 2015卷 (2015/02) Pp. 73-81

https://doi.org/10.6140/AP.9789860438437.010

並列摘要

Let X, Y be metric spaces and E, F be Banach spaces. Suppose that both X, Y are realcompact, or both E, F are realcompact. A linear bijection T between locally little Lipschitz vector-valued function spaces is said to preserve zero-set containments or nonvanishing functions if (The equation is abbreviated) or (The equation is abbreviated) respectively. Here z (f) is the zero set of a vector-valued function f. We prove that every zero-set containment preserver, and every nonvanishing function preserver when dimE=dimF ＜ +∞, is a weighted composition operator (Tf)(y)=J_yf(τ(y)). Moreover, the mapτ: Y → X is a locally little Lipschitz homeomorphism.

並列關鍵字

(generalized, locally, little) Lipschitz functions ； Zero-set containment preservers ； Biseparating maps