CENTER FOR APPLIED MATHEMATICS AND THEORETICAL PHYSICS
UNIVERZA V MARIBORU UNIVERSITY OF MARIBOR
KREKOVA 2 SI-2000 MARIBOR SLOVENIA
Phone +(386) (2) 2355 350 and 2355 351 $\bullet$ Fax +(386) (2) 2355 360
Robnik@uni-mb.si $\bullet$ www.camtp.uni-mb.si
PROF.DR. MARKO ROBNIK, DIRECTOR

Seminarsko predavanje
Centra za uporabno matematiko in teoretično fiziko

${\Large C}^{\ast }{\Large -}$ Algebras and Vidav-Palmer theorem

Prof.Dr. Joso Vukman


Department of Mathematics,
Faculty of Natural Sciences and Mathematics, University of Maribor

Abstract: Let $(A,\shortparallel . \shortparallel )$ be a Banach algebra over the complex field $\mathbf{C}.$ A mapping $x\longmapsto x^{\ast }$ on $A$ is called an involution in case $(\lambda x+\mu y)^{\ast }=\bar{\lambda}x^{\ast }+\bar{\mu}y^{\ast },(xy)^{\ast }=y^{\ast }x^{\ast }$, $(x^{\ast })^{\ast }=x$ holds for all $x,y\in A$ and all $\lambda ,\mu \in \mathbf{C}.$A Banach algebra equipped with an involution is called Banach algebra with involution. A Banach algebra with involution $(A,\shortparallel . \shortparallel )$ is $C^{\ast }-$algebra in case $\shortparallel x^{\ast }x\shortparallel =\shortparallel x\shortparallel ^{2}$ holds for all $x\in A.C^{\ast }-$algebras are important class of Banach algebras. Vidav-Palmer theorem characterizes $C^{\ast }-$algebras among all Banach algebras.

Seminarsko predavanje (v angleškem jeziku) bo v četrtek 22. januarja 2009 ob 15:15 uri v seminarski sobi CAMTP na Krekovi 2, pritličje desno. Vljudno vabljeni vsi zainteresirani, tudi študentje.

Prof.Dr. Marko Robnik
-- Direktor CAMTP --