Erratum/addendum to the paper: "Quasi *-algebras and generalized inductive limits of C*-algebras" (Studia Math. 202 (2011), 165-190)
Ideals and hereditary subalgebras in operator algebras
This paper may be viewed as having two aims. First, we continue our study of algebras of operators on a Hilbert space which have a contractive approximate identity, this time from a more Banach-algebraic point of view. Namely, we mainly investigate topics concerned with the ideal structure, and hereditary subalgebras (or HSA's, which are in some sense a generalization of ideals). Second, we study properties of operator algebras which are hereditary subalgebras in their bidual, or equivalently which...
Inductive limit algebras from periodic weighted shifts on Fock space.
Multipliers and hereditary subalgebras of operator algebras
We generalize some technical results of Glicksberg to the realm of general operator algebras and use them to give a characterization of open and closed projections in terms of certain multiplier algebras. This generalizes a theorem of J. Wells characterizing an important class of ideals in uniform algebras. The difficult implication in our main theorem is that if a projection is open in an operator algebra, then the multiplier algebra of the associated hereditary subalgebra arises as the closure...
Quasi *-algebras and generalized inductive limits of C*-algebras
A generalized procedure for the construction of the inductive limit of a family of C*-algebras is proposed. The outcome is no more a C*-algebra but, under certain assumptions, a locally convex quasi *-algebra, named a C*-inductive quasi *-algebra. The properties of positive functionals and representations of C*-inductive quasi *-algebras are investigated, in close connection with the corresponding properties of positive functionals and representations of the C*-algebras that generate the structure....
Subalgebras of graph -algebras.
Trivialization of -algebras with strongly self-absorbing fibres
Suppose is a separable unital -algebra each fibre of which is isomorphic to the same strongly self-absorbing and -injective -algebra . We show that and are isomorphic as -algebras provided the compact Hausdorff space is finite-dimensional. This statement is known not to extend to the infinite-dimensional case.