Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Author:
Gasparis Panagiotis
Supervisors info:
ΓΙΑΝΝΟΠΟΥΛΟΣ ΑΠΟΣΤΟΛΟΣ, ΚΑΘΗΓΗΤΗΣ, ΤΜΗΜΑ ΜΑΘΗΜΑΤΙΚΩΝ, ΕΚΠΑ
Original Title:
ΧΩΡΟΙ BANACH ΣΥΝΕΧΩΝ ΣΥΝΑΡΤΗΣΕΩΝ
Translated title:
BANACH SPACES OF CONTINUOUS FUNCTIONS
Summary:
This dissertation consists of two parts:
In the first part we will focus on C(K) spaces, where K is a compact Hausdorff
topological space, and we will study their properties as Banach spaces. We will
focus on which common Banach spaces are C(K) spaces (in terms of isometric isomorphism) and their classification under linear isomorphism. We will also study the weak-compactness of subsets and operators in C(K) spaces but also in L1 (μ).
In the second part we will talk about vector measures, ie measures valued in a
Banach space and we will try to determine under what conditions we can have a vector Radon-Nikodym theorem and what are the properties of the spaces in which such a theorem holds.
Main subject category:
Science
Keywords:
Banach spaces, bounded linear operators, vector measures, metric spaces, compactness, C(K), isometrically injective, order-complete, Miljutin, Goodner-Nachbin, Dunford-Pettis, Radon-Nikodym Property
