An amenable von Neumann algebra is an injective von Neumann algebra. Injectivity means that
completely positive contractive maps from operator subsystems into the algebra extend
to larger operator systems with the same properties.
Equivalently, in a faithful representation
on a Hilbert space 
, there is a norm-one projection from 
onto the algebra. Finite-dimensional
von Neumann algebras are examples. The relative
bicentralizer problem asks for expected amenable subalgebras retaining a specified
commutant in the continuous core.
Amenable von Neumann Algebra
See also
Completely Positive Map, Continuous Core, Operator Algebra Conditional Expectation, von Neumann AlgebraExplore with Wolfram|Alpha
References
Anantharaman, C. and Popa, S. An Introduction to
Factors. https://www.math.ucla.edu/~popa/Books/IIun.pdf.
Cite this as:
Weisstein, Eric W. "Amenable von Neumann Algebra." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AmenablevonNeumannAlgebra.html