The Vidav-Palmer theorem and C*-equivalent algebras

Μπαζιώτης, Γεώργιος; Baziotis, Georgios

dc.contributor.author	Μπαζιώτης, Γεώργιος	el
dc.contributor.author	Baziotis, Georgios	en
dc.date.accessioned	2021-05-17T18:39:04Z
dc.date.available	2021-05-17T18:39:04Z
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/53437
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.21135
dc.description	Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Εφαρμοσμένες Μαθηματικές Επιστήμες”	el
dc.rights	Default License
dc.subject	Εφαρμοσμένες μαθηματικές επιστήμες	el
dc.subject	Συναρτησιακή ανάλυση	el
dc.subject	Θεωρία τελεστών	el
dc.subject	C*-άλγεβρες	el
dc.subject	Άλγεβρες banach	el
dc.subject	Operator theory	en
dc.subject	Applied mathematical sciences	en
dc.subject	Functional analysis	en
dc.subject	C*-algebras	en
dc.subject	Banach algebras	en
dc.title	The Vidav-Palmer theorem and C*-equivalent algebras	en
dc.title	Το Θεώρημα Vidav-Palmer και οι C*-ισοδύναμες άλγεβρες	el
heal.type	masterThesis
heal.classification	Μαθηματικά	el
heal.classification	Mathematics	en
heal.language	en
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2021-03-05
heal.abstract	Over the last century, the mathematical area of Operator Algebras has gained a lot of attention among mathematicians, thanks to the numerous applications on Natural Sciences. The most famous mathematical object on this area are C-algebras. Primarily used to model the algebra of observables in quantum mechanics, a C-algebra is a very well behaved structure with which a mathematician can approach many problems in Mathematics. This great behavior is the fact from which the purpose of this thesis arises. Unlike the previous, the more general object called Banach algebra is not that well behaved. Therefore, the purpose of this Master’s thesis is to present some conditions in order for an arbitrary Banach or -Banach algebra to be a C-algebra. In the first chapter, which is an introduction to Banach algebras, we provide the essential concepts and tools in order to continue. In the second chapter we introduce the concept of an involutive Banach algebra and demonstrate the characterization of hermitian and symmetric -Banach algebras, with the celebrated Shiralli-Ford Theorem and provide some useful results rising from Pt´ak’s Inequality. Also a brief presentation regarding M¨obius Transformations takes place, necessary to prove the Russo-Dye Theorem. In the third chapter, after the description of the concept of the Numerical Range is displayed, we find ourselves in a position to provide the first major result, the Vidav-Palmer Theorem. In the last chapter, we provide some well-known results on C-algebras such as the Gelfand-Naimark Theorem and introduce the reader to the concept of C-equivalent algebras. After the presentation of some early results by B. A. Barnes, we conclude with J. Cuntz’s ingenious proof that local C-equivalence implies C*-equivalence.	en
heal.advisorName	Γιαννακάκης, Νικόλαος	el
heal.advisorName	Yannakakis, Nikolaos	en
heal.committeeMemberName	Γιαννακάκης, Νικόλαος	el
heal.committeeMemberName	Δριβαλιάρης, Δημοσθένης	el
heal.committeeMemberName	Ανούσης, Μιχαήλ	el
heal.committeeMemberName	Yannakakis, Nikolaos	en
heal.committeeMemberName	Drivaliaris, Dimosthenis	en
heal.committeeMemberName	Anousis, Michael	en
heal.academicPublisher	Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Εφαρμοσμένων Μαθηματικών και Φυσικών Επιστημών	el
heal.academicPublisherID	ntua
heal.numberOfPages	80 σ.	el
heal.fullTextAvailability	false