Open partial isometries and positivity in operator spaces

• Autorzy: David P. Blecher , Matthew Neal
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46L07: Operator spaces and completely bounded maps
• 46A40: Ordered topological linear spaces, vector lattices
• 46L08: C * -modules
• 47B60: Operators on ordered spaces
• 47L07: Convex sets and cones of operators
• 47L05: Linear spaces of operators
• 46B40: Ordered normed spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 182
• Numer: 3
• Strony: 227-262

Daty

wydano

2007

Twórcy

autor

David P. Blecher

• Department of Mathematics, University of Houston, Houston, TX 77204-3008, U.S.A.

autor

Matthew Neal

• Department of Mathematics, Denison University, Granville, OH 43023, U.S.A.

Identyfikatory

DOI

10.4064/sm182-3-4