Generalizations of Sobczyk's Theorem for C(K) Banach spaces

• Grant number: 19/08515-6
• Support Opportunities: Scholarships abroad - Research
• Start date: January 05, 2020
• End date: January 04, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Claudia Correa de Andrade Oliveira
• Grantee: Claudia Correa de Andrade Oliveira
• Host Investigator: Wieslaw Kubis
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil
• Institution abroad: Czech Academy of Sciences (CAS), Czech Republic

Abstract

The general goal of this project is the investigation of two classical problems of the Geometry of Banach Spaces in the context of C(K) spaces: the extension of bounded operators and the complementation of subspaces. Due to Sobczyk's Theorem the space c_0 plays an essential role in this investigation. Sobczyk's Theorem ensures that if X is a separable Banach space then every c_0-valued bounded operator defined on a closed subspace of X admits a bounded extension to X and therefore every isomorphic copy of c_0 in X is complemented. The search for generalizations of Sobczyk's Theorem for nonseparable Banach spaces has attracted the community's attention in recent decades and has proven to be a fertile field of research. In this project we intend to investigate generalizations of Sobczyk's Theorem for nonseparable C(K) spaces. With this purpose, we will study the phenomena of the extension of c_0-valued bounded operators and of the complementation of isomorphic copies of c_0 in the spaces of continuous functions of many classes of nonmetrizable compact spaces. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

CORREA, CLAUDIA; RUSSO, TOMMASO; SOMAGLIA, JACOPO. Small semi-Eberlein compacta and inverse limits. Topology and its Applications, v. 302, OCT 1 2021. (18/09797-2, 19/08515-6)

CORREA, CLAUDIA; CUTH, MAREK; SOMAGLIA, JACOPO. haracterization of (semi-)Eberlein compacta using retractional skeleton. STUDIA MATHEMATICA, v. 263, n. 2, NOV 2021. (19/08515-6, 18/09797-2)

CORREA, CLAUDIA; CUTH, MAREK; SOMAGLIA, JACOPO. Characterizations of weakly K-analytic and Vasak spaces using projectional skeletons and separable PRI. Journal of Mathematical Analysis and Applications, v. 515, n. 1, p. 25-pg., 2022-06-08. (18/09797-2, 19/08515-6)