2023/09/01 by Ferenczi, Valentin, Rincón-Villamizar, Michael A.
#46A22 #54H20 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46B04 #secondary 37B05
paper · doi:10.48550/arxiv.2309.00185
Continuing with the study of Approximately ultrahomogeneous and Fraïssé Banach spaces introduced by V. Ferenczi, J. López-Abad, B. Mbombo and S. Todorcevic, we define formally weaker and in some aspects more natural properties of Banach spaces which we call Almost ultrahomogeneity and the Almost Fraïssé Property. We obtain relations between these different homogeneity properties of a space E and relate them to certain pseudometrics on the class Age(E) of finite dimensional subspaces of E. We prove that ultrapowers of an almost Fraïssé Banach space are ultrahomogeneous. We also study two properties called finitely isometrically extensible and almost finitely isometrically extensible, respectively, and prove that approximately ultrahomogeneous Banach spaces are finitely isometrically extensible.