Open partial isometries and positivity in operator spaces

. O A ] 2 7 Ju n 20 06 OPEN PARTIAL ISOMETRIES AND POSITIVITY IN OPERATOR SPACES

We study positivity in C*-modules and operator spaces using open tripotents, and an ordered version of the 'noncommutative Shilov boundary'. Because of their independent interest, we also systematically study open tripo-tents and their properties.

. O A ] 1 A ug 2 00 7 OPEN PARTIAL ISOMETRIES AND POSITIVITY IN OPERATOR SPACES

We first study positivity in C*-modules using tripotents (= partial isometries) which are what we call open. This is then used to study ordered operator spaces via an ‘ordered noncommutative Shilov boundary’ which we introduce. This boundary satisfies the usual universal diagram/property of the noncommutative Shilov boundary, but with all the ‘arrows’ completely positive. Because of their indep...

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