Factorization of Completely Bounded Bilinear Operators and Injectivity
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A completely bounded bilinear operatorφ:M×M→M on a von Neumann algebra M is said to have a factorization in M if there exist completely bounded linear operatorsψj, θj:M→M such thatφ(x, y)=sum;j∈Λψj(x)θj(y),x, y∈M,where convergence of the sum is made precise below. The main result of the paper is that all completely bounded bilinear operatorsφ:M×M→M have factorizations in M if and only if M is injective. © 1998 Academic Press.
author list (cited authors)
Sinclair, A. M., & Smith, R. R.
complete list of authors
Sinclair, Allan M||Smith, Roger R