Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Author:
Paraskevas Ioannis-Apollon
Supervisors info:
Κατάβολος Αριστείδης, Ομότιμος Καθηγητής, Τμήμα Μαθηματικών, Σχολή Θετικών Επιστημών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Γιαννόπουλος Απόστολος, Καθηγητής, Τμήμα Μαθηματικών, Σχολή Θετικών Επιστημών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Ανούσης Μιχαήλ, Καθηγητής, Τμήμα Μαθηματικών, Σχολή Θετικών Επιστημών, Πανεπιστήμιο Αιγαίου
Original Title:
Operator algebras associated with C *-dynamical systems and C *-correspondences
Translated title:
Operator algebras associated with C *-dynamical systems and C *-correspondences
Summary:
The aim of the present thesis is to describe certain operator algebras associated with C*-dynamical systems and C*-correspondences. We introduce the notion of the crossed product of a C*-algebra by a discrete group and we study in detail the case of the integers. We give necessary and
sufficient conditions, when the C*-algebra is the algebra of continuous functions on a
compact Hausdorff topological space, for the crossed product to be simple. Furthermore, we introduce the notion of the semi-crossed product and we give alternative descriptions of its norm when the C*-dynamical system is induced by a ∗-automorphism. In addition, we study C*-correspondences and their representations and we prove the Gauge-Invariance Uniqueness theorem. Finally, we use results
and tools that we have developed so far, in order to identify the C*-envelope of the semi-crossed
product and the C*-envelope of the tensor algebra of a C*-correspondence.
Main subject category:
Science
Keywords:
C*-algebras, Operator algebras, C*-correspondences,Crossed products,Semi-crossed products
