Postgraduate Thesis uoadl:3176578 191 Read counter

Κατεύθυνση Θεωρητικά Μαθηματικά

Library of the School of Science

Library of the School of Science

2022-04-04

2022

Gasparis Panagiotis

ΓΙΑΝΝΟΠΟΥΛΟΣ ΑΠΟΣΤΟΛΟΣ, ΚΑΘΗΓΗΤΗΣ, ΤΜΗΜΑ ΜΑΘΗΜΑΤΙΚΩΝ, ΕΚΠΑ

ΧΩΡΟΙ BANACH ΣΥΝΕΧΩΝ ΣΥΝΑΡΤΗΣΕΩΝ

Greek

BANACH SPACES OF CONTINUOUS FUNCTIONS

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.

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.

Science

Banach spaces, bounded linear operators, vector measures, metric spaces, compactness, C(K), isometrically injective, order-complete, Miljutin, Goodner-Nachbin, Dunford-Pettis, Radon-Nikodym Property

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