Coordinates for analytic operator algebras

Operator Algebras for Analytic Varieties

We study the isomorphism problem for the multiplier algebras of irreducible complete Pick kernels. These are precisely the restrictionsMV of the multiplier algebraM of Drury-Arveson space to a holomorphic subvariety V of the unit ball. We find thatMV is completely isometrically isomorphic toMW if and only if W is the image of V under a biholomorphic automorphism of the ball. In this case, the i...

0 A functional - analytic theory of vertex ( operator ) algebras , II

For a finitely-generated vertex operator algebra V of central charge c ∈ C, a locally convex topological completion HV is constructed. We construct on HV a structure of an algebra over the operad of the c 2 -th power Det c/2 of the determinant line bundle Det over the moduli space of genus-zero Riemann surfaces with ordered analytically parametrized boundary components. In particular, HV is a m...

Operator Algebras

Notice that the left-hand side of the third equation is the sum of the left-hand sides of the first two. As a result, no solution to the system exists unless a + b = c. But if a + b = c, then any solution of the first two equations is also a solution of the third; and in any linear system involving more unknowns than equations, solutions, when they exist, are never unique. In the present case, ...

Operator Theory and Operator Algebras

Boundary Representations for Operator Algebras

All operator algebras have (not necessarily irreducible) boundary representations. A unital operator algebra has enough such boundary representations to generate its C-envelope.