Algebraic reflexivity of the isometry group of some spaces of Lipschitz functions

作者：Jimenez Vargas A^*; Morales Campoy A; Villegas Vallecillos Moises

来源：Journal of Mathematical Analysis and Applications, 2010, 366(1): 195-201.

DOI：10.1016/j.jmaa.2010.01.034

• Iso-reflexive space
• Algebraic reflexivity
• Isometry group
• Lipschitz function
• Isometric reflection
• Generalized bi-circular projection

We show that the isometry groups of Lip(X, d) and lip(X, d(alpha)) with alpha is an element of (0, 1), for a compact metric space (X. d), are algebraically reflexive. We also prove that the sets of isometric reflections and generalized bi-circular projections on such spaces are algebraically reflexive. In order to achieve this, we characterize generalized bi-circular projections on these spaces.

• 出版日期2010-6-1