Operator Algebras¶

7 domain-specific abstractions whose origin domain is Operator Algebras.

Baum–Connes Conjecture — An assembly-map conjecture relating a group's geometric equivariant K-homology to the analytic K-theory of its reduced group C-star algebra.
Calkin algebra — The C*-algebra obtained by quotienting all bounded operators on an infinite-dimensional separable Hilbert space by the ideal of compact operators.
Jordan operator algebra — A normed Jordan algebra modeled on self-adjoint operators with the symmetrized product a circle b equal to one half of ab plus ba.
Nuclear C*-algebra — A C-algebra whose algebraic tensor product with every C-algebra has a unique C*-norm, equivalently whose identity approximately factors through matrix algebras by completely positive maps.
Quasitrace — A positive tracial functional on a C-star algebra that is homogeneous and additive on commuting positive elements but need not be globally additive.
Tomita–Takesaki theory — The modular theory deriving a one-parameter automorphism group and commutant duality from a von Neumann algebra with a cyclic separating vector or faithful normal weight.
Ultrastrong topology — A locally convex operator topology on bounded operators generated by seminorms obtained from countable square-summable families of Hilbert-space vectors or positive normal functionals.