Autor(es)

Ferenczi, Valentin ; Rincon-Villamizar, Michael A.

• Tipo de documento: Artigo Científico
• Fonte: Israel Journal of Mathematics; v. N/A, p. 35-pg., 2025-07-30.

Resumo

Continuing with the study of approximately ultrahomogeneous and Fra & iuml;ss & eacute; Banach spaces introduced by V. Ferenczi, J. L & oacute;pez-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 Fra & iuml;ss & eacute; 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 Fra & iuml;ss & eacute; Banach space are ultrahomogeneous. We also study two properties called finitely isometrically extensible and almost finitely isometrically extensible, respectively, and prove that approximately ultrahomogeneous reflexive Banach spaces are finitely isometrically extensible.Finally, we study oligomorphy in Banach spaces, and give a proof that a Banach space is Fra & iuml;ss & eacute; if and only if it is approximately ultrahomogeneous and oligomorphic. (AU)

• Processo FAPESP: 16/25574-8 - Geometria dos espaços de Banach
• Beneficiário: Valentin Raphael Henri Ferenczi
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 21/01144-2 - Ideais associados a sequências em espaços de Banach e derivações Lipschitz em espaços de Hilbert
• Beneficiário: Michael Alexánder Rincón Villamizar
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado