The first difference between the pure algebraic and the

operator algebra context appeared in the definition of the partial skew group algebra, which is not automatically associative in the general situation.

Zuevsky, "A generalized vertex

operator algebra for Heisenberg intertwiners," Journal of Pure and Applied Algebra, vol.

Let n > 1 be an integer, let A be a unital

operator algebra on a Hilbert space H with unit I, and let [alpha], [beta] be automorphisms on A.

i.e., for any f [member of] [M.sub.p], the image [[alpha].sup.p] (f) is a multiplication operator on [H.sub.p] with its symbol f contained in the

operator algebra B([H.sub.p]) of all (bounded linear) operators on [H.sub.p].

Akemann, The dual space of an

operator algebra. Trans.

Originally published in Japanese for a Surveys in Geometry workshop held in Tokyo, Japan, in 1998, this translation offers an overview of

operator algebra theory.

Davidson, Fuller, and Kakariadis examine the semicrossed products of a semigroup action by *-endomorphisms on a C*-algebra, or more generally of an action on an arbitrary

operator algebra by completely contractive endomorphisms.

First, note that the

operator algebra B([X.sup.**]) can be identified with the dual space [([X.sup.**])[??][X.sup.*]).sup.*] of the projective tensor product [X.sup.**][??][X.sup.*] in a natural way; see for example Corollary VIII.2.2 of [5].

Most of the book can be read with only a basic knowledge of functional analysis; however, some experience in the theory of

operator algebra is helpful.

From an August 2016 combination summer school and conference at Tohoku University in Japan, a survey article and 11 research articles explore

operator algebras and mathematical physics.