Geodesic
Open partial isometries and positivity in operator spaces
David P. Blecher1 ; Matthew Neal2
1Department of Mathematics University of Houston Houston, TX 77204-3008, U.S.A.
2Department of Mathematics Denison University Granville, OH 43023, U.S.A.
Studia Mathematica, Tome 182 (2007) no. 3, pp. 227-262
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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 independent interest, we also systematically study open tripotents and their properties.
DOI : 10.4064/sm182-3-4
Keywords: first study positivity * modules using tripotents partial isometries which what call study ordered operator spaces via ordered noncommutative shilov boundary which introduce boundary satisfies usual universal diagram property noncommutative shilov boundary arrows completely positive because their independent interest systematically study tripotents their properties

David P. Blecher  1   ; Matthew Neal  2

1 Department of Mathematics University of Houston Houston, TX 77204-3008, U.S.A.
2 Department of Mathematics Denison University Granville, OH 43023, U.S.A. 
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David P. Blecher; Matthew Neal. Open partial isometries and positivity
 in operator spaces. Studia Mathematica, Tome 182 (2007) no. 3, pp. 227-262. doi: 10.4064/sm182-3-4

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