Bohaté systémy projekcí a retrakcí

• Main Author: Somaglia, Jacopo
• Other Authors: Kalenda, Ondřej
• Format: Doctoral Thesis
• Language: English
• Published: 2018
• Online Access: http://www.nusl.cz/ntk/nusl-392401

Title: Rich Families of Projections and Retractions Author: Jacopo Somaglia Department: Department of Mathematical Analysis MFF UK (Prague), Department of Mathematics Università degli Studi di Milano (Milan) Supervisors: Prof. RNDr. Ondřej Kalenda PhD DSc. Department of Mathematical Analysis MFF UK (Prague), Prof. Dr. Clemente Zanco Department of Mathematics Università degli Studi di Milano (Milan) Abstract: We deal with problems on non-separable Banach spaces and non-metrizable compact spaces. In particular these problems concern Banach spaces with a projectional skeleton and compact spaces with a retractional skeleton. A projectional (resp. retractional) skeleton is a family of continuous projections (resp. retractions) on a Banach (resp. compact) space, which satisfies certain compatibility properties. Banach spaces with projectional skeleton and compact spaces with retractional skeleton can be viewed as non-commutative version of Plichko Banach spaces and Valdivia compact spaces respectively. The thesis is split into three chapters. Each chapter consists of a submitted/published paper concerning different problems in this area. In the first chapter, On the class of continuous images of non-commutative Valdivia compacta, we investigate the stability of some topological properties in the class of weakly...