On von Neumann algebras which are complemented subspaces of B(H)
Erik Christensen, Allan M. Sinclair
TL;DR
This paper investigates the conditions under which von Neumann algebras, as complemented subspaces of B(H), are injective, focusing on the existence of bounded and completely bounded projections.
Contribution
It establishes that the existence of certain projections implies the injectivity of the von Neumann algebra, extending known results to broader cases.
Findings
Existence of a completely bounded projection implies M is injective.
Bounded projections onto properly infinite M also imply injectivity.
Results connect the structure of projections with algebra injectivity.
Abstract
If there exists a completely bounded projection of B(H) onto a von Neumann algebra M on H, then M is injective. If there exists a bounded projection and M is properly infinite, the same conclusion holds.
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Operator Algebra Research · Advanced Banach Space Theory