Concrete realizations of quotients of operator spaces

Details Concrete realizations of quotients of operator spaces Concrete realizations of quotients of operator spaces

2011-01-15

arxiv.org/abs/1101.3012v2

Mathematics

Operator Algebras

12 pages. Version 2: Short section added concerning quotients of operator systems. Various small improvements made

Scientific paper

Let B be a unital C*-subalgebra of a unital C*-algebra A, so that A/B is an abstract operator space. We show how to realize A/B as a concrete operator space by means of a completely contractive map from A into the algebra of operators on a Hilbert space, of the form a maps to [z, a] where z is a Hermitian unitary operator. We do not use Ruan's theorem concerning concrete realization of abstract operator spaces. Along the way we obtain corresponding results for abstract operator spaces of the form A/V where V is a closed subspace of A, and then for the more special cases in which V is a *-subspace or an operator system.

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