Set-theoretic topological methods on operators on Banach spaces of the form C(K)

• Grant number: 10/17853-8
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: March 01, 2011
• End date: November 30, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Christina Brech
• Grantee: Claudia Correa de Andrade Oliveira
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

Several properties of compact Hausdorff spaces K depend on infinitary combinatorics. Frequently, this dependency passes also to the Banach space of continuous functions C(K). In this project our purpose is to study this kind of dependency, specially in what concerns the properties of linear operators ons spaces of the form C(K). We plan to start from known properties of compact non metrizable spaces K to study the properties of the corresponding C(K), but whenever it is necessary and possible, we will work on results about compact spaces as well. An analysis of the behaviour of adjoint operators will be of great value, since they provide a link between operators and continuous functions on compact spaces. Projections, being an important type of operators, will be particularly analyzed. Therefor, we will work also with decompositions of Banach spaces C(K). The project will be coordinated by Profs. Christina Brech and Piotr Koszmider (who will be officialized as a co-advisor at IME-USP). The candidate plans to develop part of the project in Poland, working directly with Prof. Koszmider.

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; TAUSK, DANIEL V.. On extensions of c(0)-valued operators. Journal of Mathematical Analysis and Applications, v. 405, n. 2, p. 400-408, SEP 15 2013. (10/17853-8)