Supervisors info:
Χαραλαμπίδου Μαρίνα Αναπληρώτρια Καθηγήτρια, Τσέρτος Ιωάννης Αναπληρωτής Καθηγητής, Νταουλτζή-Μαλάμου Ζωή Λέκτορας
Summary:
ABSTRACT
In this work, we study left, right, and two-sided multipliers of a complex
(topological)
algebra. For a proper commutative topological algebra (separately continuous
multiplication) we give a relation between the multipliers of it, and the set of
all continuous complex functions on its global spectrum. We also refer to
conditions,
under which, a compact multiplier of a complete metrizable locally convex
algebra turns to be the trivial one. Further, we study double multipliers of a
topological
algebra along with algebraic properties of them. Taking the algebra Μ(Α)
of the continuous double multipliers of a locally C*-algebra A, we endow
it with an involution and two topologies (called the topology of seminorms and
the
strict topology, respectively). Under the first topology, the bounded elements
of M(A)
is (algebraically) identical with the algebra of all continuous double
multipliers,
defined on the algebra b(A) of the bounded elements of the initial algebra.
Finally, we deal with locally m-convex *-algebras (A, τ) with continuous
involution,
which are perfect topological algebras. In this context, we describe the algebra
of multipliers, when A as before, is a locally C*-algebra, under a weaker
topology
than τ. The same is applied in case A is a certain locally convex H*-algebra.
Keywords:
Locally C*-algebra, (left, right) multiplier, multiplier algebra, Arens-Michael decomposition
