Ein operatorwertiger Hahn-Banach Satz |
| |
Authors: | Gerd Wittstock |
| |
Affiliation: | Fachbereich Mathematik, Universität des Saarlandes, D 6600 Saarbrücken, West Germany |
| |
Abstract: | We generalize Arveson's extension theorem for completely positive mappings [1] to a Hahn-Banach principle for matricial sublinear functionals with values in an injective C1-algebra or an ideal in B(). We characterize injective W1-algebras by a matricial order condition. We illustrate the matricial Hahn-Banach principle by three applications: (1) Let be unital C1-algebras, a subalgebra of and injective. If ?: → is a completely bounded self-adjoint -bihomomorphism, then it can be expressed as the difference of two completely positive -bihomomorphism. (2) Let be a W1-algebra, containing 1, on a Hilbert space . If is finite and hyperfinite, there exists an invariant expectation mapping P of B() onto ′. P is an extension of the center trace. (3) Combes [7] proved, that a lower semicontinuous scalar weight on a C1-algebra is the upper envelope of bounded positive functionals. We generalize this result to unbounded completely positive mappings with values in an injective W1-algebra. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|