@MISC{KANEDA09extremepoints, author = {MASAYOSHI KANEDA}, title = {Extreme Points of the Unit Ball . . . }, year = {2009} }

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Abstract

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.