Induced and reduced unbounded operator algebras

Bicommutants of Reduced Unbounded Operator Algebras

The unbounded bicommutant (ME′ ) ′′ wc of the reduction of an O*algebra Mvia a given projection E weakly commuting with M is studied, with the aim of finding conditions under which the reduction of a GW*-algebra is a GW*-algebra itself. The obtained results are applied to the problem of the existence of conditional expectations on O*-algebras.

Conditional Expectations for Unbounded Operator Algebras

Two conditional expectations in unbounded operator algebras (O∗-algebras) are discussed. One is a vector conditional expectation defined by a linear map of an O∗-algebra into the Hilbert space on which the O∗-algebra acts. This has the usual properties of conditional expectations. This was defined by Gudder and Hudson. Another is an unbounded conditional expectation which is a positive linear m...

Operator Theory and Operator Algebras

Induced modules for vertex operator algebras

For a vertex operator algebra V and a vertex operator subalgebra V ′ which is invariant under an automorphism g of V of finite order, we introduce a g-twisted induction functor from the category of g-twisted V ′-modules to the category of g-twisted V -modules. This functor satisfies the Frobenius reciprocity and transitivity. The results are illustrated with V ′ being the g-invariants in simple...

Operator algebras and topology