Supervisors info:
Μαρίνα Χαραλαμπίδου Αναπλ. Καθηγ. (Επιβλέπουσα),Μαρία Φραγκουλοπούλου Καθηγ.,Ιωάννης Τσέρτος Αναπλ. Καθηγ.
Summary:
This work refers to Michael's Conjecture which is about functional continuity
of a commutative Frechet locally m-convex algebra. It is proved that every
commutative symmetric Frechet locally m-convex algebra is functionally
continuous. Moreover, the concepts of dense stongly dense inverse limit rings
are described, and results relevant to them are given. Also, for unitary
commutative Frechet locally m-convex algebras, conditions are given which
ensure their functional continuity. Additionally, it is proved that Michael's
Conjecture is aquivalent to the boundedness of linear multiplicative
functionals of a commutative Frechet locally m-convex algebra. Furthermore, we
study the class of Frechet locally m-convex algebras with orthogonal bases and
it is proved that it has the property of funtional continuity.In addition,
through the theory of compex functions of several complex variables, we refer
to a relation which gives positive answer to Michael's Conjecture if it holds
true. Finally, alternative proofs of already known results and other
conclusions are given, using Do Sin Sya's technique.
Keywords:
Funtionally continuous topological algebra, Frechet locally m-convex algebra, Symmetric algebra , Orthogonal basis, Do Sin Sya technique
