Isometries of certain reflexive operator algebras

Derivations of Certain Operator Algebras

Let be a nest and let be a subalgebra of L(H) containing all rank one operators of alg . We give several conditions under which any derivation δ from into L(H) must be inner. The conditions include (1) H− ≠H, (2) 0+ ≠ 0, (3) there is a nontrivial projection in which is in , and (4) δ is norm continuous. We also give some applications.

Some Problems concerning Reflexive Operator Algebras

We discuss below some problems concerning a certain class of algebras of operators on complex Banach space. Each algebra of the class arises from a lattice of subspaces of the underlying space (in a way that will soon be made precise) and most of the problems are of the fonn: find conditions, additional to those specified a priori, on the lattice of subspaces, which are both necessary and suffi...

Derivations and Automorphisms of Certain Operator Algebras

Certain Free Products of Graph Operator Algebras

We develop a notion of a generalized Cuntz-Krieger family of projections and partial isometries where the range of the partial isometries need not have trivial intersection. We associate to these generalized Cuntz-Krieger families a directed graph, with a coloring function on the edge set. We call such a directed graph an edge-colored directed graph. We then study the C∗algebras and the non-sel...

Certain extensions of vertex operator algebras of affine type

We generalize Feigin and Miwa’s construction of extended vertex operator (super)algebras Ak(sl(2)) for other types of simple Lie algebras. For all the constructed extended vertex operator (super)algebras, irreducible modules are classified, complete reducibility of every module is proved and fusion rules are determined modulo the fusion rules for vertex operator algebras of affine type.