2004/08/18 by Masayoshi Kaneda, Kaneda, Masayoshi
Mathematics · #46L05 (Secondary) #46L07 #46M10 #47L07 (Primary) #47L25 #47L30 #47L50 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:46L05 #msc:46L07 #msc:46M10 #msc:47L07 #msc:47L25 #msc:47L30 #msc:47L50
paper · pdf · doi:10.48550/arxiv.math/0408235
27 pages, http://www.math.uci.edu/~mkaneda/
arxiv created 2009/05/18 · arxiv updated 2009/12/01
This paper is a revision and an enlargement of the previous version titled "Extreme points of the unit ball of a quasi-multiplier space" which had been circulated since 2004. We study extreme points of the unit ball of an operator space by introducing the new notion (approximate) "quasi-identities". Then we characterize an operator algebra with a contractive approximate quasi- (respectively, left, right, two-sided) identity in terms of quasi-multipliers and extreme points. Furthermore, we give a very neat necessary and sufficient condition for a given operator space to become a C^*-algebra or a one-sided ideal in a C^*-algebra in terms of quasi-multipliers. An extreme point is also used to show that any TRO with predual can be decomposed to the direct sum of a two-sided ideal, a left ideal, and a right ideal in some von Neumann algebra.