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Near Inclusion of Operator Algebras

A near inclusion of operator algebras M,N subset= B(H) is a uniform approximation of the closed unit ball of M by elements of N in the operator norm. Its one-sided gap is

gamma(M,N)=sup_(x in M ||x||<=1)inf_(y in N)||x-y||.

The approximating element y need not have norm at most 1. There is no requirement on the reverse gap gamma(N,M).

See also

Kadison-Kastler Conjecture, Kadison-Kastler Distance, Unitary Transformation, von Neumann Algebra

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References

Christensen, E. "Near Inclusions of C^*-Algebras." Acta Math. 144, 249-265, 1980. https://doi.org/10.1007/BF02392125.

Cite this as:

Weisstein, Eric W. "Near Inclusion of Operator Algebras." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NearInclusionofOperatorAlgebras.html

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