Unit:
Τομέας Μαθηματικής ΑνάλυσηςLibrary of the School of Science
Author:
Καμπούκος Κυριάκος
Dissertation committee:
Σ. Μερκουράκης Καθηγητής (Επιβλέπων), Σ. Αργυρός Καθηγητής, Γ. Κουμουλλής Καθηγητής
Original Title:
Τοπολογικές ιδιότητες χώρων Banach
Summary:
The subject of this thesis is the study of some properties of the weak
topology of Banach spaces, which are of descriptive character in the sense of
Choquet.
In the first Chapter are introduced the concepts of the strongly countably
determined topological space, as well as the strongly Κσδ subset of a
topological space and that of the compact covering upper semicontinuous compact
valued map. Furthermore, we give some characterizations of the above classes of
spaces analogous to the classical characterizations of K-analytic and countably
determined spaces.
In the second Chapter is defined and studied a class of Banach spaces, which
are strongly countably determined in their weak topology and are called
strongly weakly countably determined (SWCD). This class is the analogue of the
class of WCD Banach spaces of Vasak, is contained in it and does not contain
all separable Banach spaces.
In the third Chapter two comparable and distinct subclasses of the class of
SWKA Banach spaces are studied. The first one is defined by weakening the
definition of SWCG Banach space given by Schluchterman and Wheeler. This new
class contains properly the SWCG Banach spaces and inherits their basic
properties. The second subclass contains the previous one properly and consists
of those Banach spaces which are strongly Κσδ in their second dual, endowed
with the weak* topology.
Keywords:
strongly countably determined, strongly Κσδ, strongly K-analytic, compact covering map, SWCD Banach spaces
Number of pages:
viii, 84
