caa a22 4500 467882762 CHVBK 20180406152725.0 cr unu---uuuuu 170328e20060401xx s 000 0 eng 10.1007/s10485-006-9012-0 doi (NATIONALLICENCE)springer-10.1007/s10485-006-9012-0 Bounded and Unitary Elements in Pro- C *-algebras [Elektronische Daten] [Rachid El Harti, Gábor Lukács] A pro-C*-algebra is a (projective) limit of C*-algebras in the category of topological *-algebras. From the perspective of non-commutative geometry, pro-C*-algebras can be seen as non-commutative k-spaces. An element of a pro-C*-algebra is bounded if there is a uniform bound for the norm of its images under any continuous *-homomorphism into a C*-algebra. The *-subalgebra consisting of the bounded elements turns out to be a C*-algebra. In this paper, we investigate pro-C*-algebras from a categorical point of view. We study the functor (−) b that assigns to a pro-C*-algebra the C*-algebra of its bounded elements, which is the dual of the Stone-Čech-compactification. We show that (−) b is a coreflector, and it preserves exact sequences. A generalization of the Gelfand duality for commutative unital pro-C*-algebras is also presented. Springer Science + Business Media B.V., 2006 pro- C *-algebra nationallicence Gelfand duality nationallicence Stone-Čech-compactification nationallicence Tychonoff space nationallicence strongly functionally generated nationallicence k -space nationallicence k R -space nationallicence bounded nationallicence spectrally bounded nationallicence coreflection nationallicence exact nationallicence El Harti Rachid Department of Mathematics, University Hassan I, FST de Settat, BP 577, 2600, Settat, Morocco aut Lukács Gábor Department of Mathematics and Statistics, Dalhousie University, B3H 3J5, Halifax, Nova Scotia, Canada aut Applied Categorical Structures Kluwer Academic Publishers 14/2(2006-04-01), 151-164 0927-2852 14:2<151 2006 14 10485 https://doi.org/10.1007/s10485-006-9012-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10485-006-9012-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- El Harti Rachid Department of Mathematics, University Hassan I, FST de Settat, BP 577, 2600, Settat, Morocco aut NATIONALLICENCE 700 1- Lukács Gábor Department of Mathematics and Statistics, Dalhousie University, B3H 3J5, Halifax, Nova Scotia, Canada aut NATIONALLICENCE 773 0- Applied Categorical Structures Kluwer Academic Publishers 14/2(2006-04-01), 151-164 0927-2852 14:2<151 2006 14 10485 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer