Expectations in an operator algebra

The Measure Algebra as an Operator Algebra

Introduction. In § I, it is shown that M(G)*, the space of bounded linear functionals on M(G), can be represented as a semigroup of bounded operators on M(G). Let A denote the non-zero multiplicative linear functionals on M(G) and let P be the norm closed linear span of A in M(G)*. In § II, it is shown that P , with the Arens multiplication, is a commutative J3*-algebra with identity. Thus P = ...

The Ideal Envelope of an Operator Algebra

A left ideal of any C∗-algebra is an example of an operator algebra with a right contractive approximate identity (r.c.a.i.). Conversely, we show here and in [6] that operator algebras with r.c.a.i. should be studied in terms of a certain left ideal of a C∗-algebra. We study operator algebras and their multiplier algebras from the perspective of ‘Hamana theory’ and using the multiplier algebras...

The Dual Space of an Operator Algebra

Introduction. The purpose of this paper is to study noncommutative C*algebras as Banach spaces. The Gelfand representation of an abelian C*-algebra as the algebra of all continuous complex-valued functions on its spectrum has made it possible to apply the techniques of measure theory and the topological properties of compact Hausdorff spaces to the study of such algebras. No such structure theo...

Adjoining a Unit to an Operator Algebra

We show that the matricial norms of a non-unital operator algebra determine those of the algebra obtained by adjoining a unit to it. As applications , we classify two-dimensional unital operator algebras and show that the algebra of bounded holomorphic functions on a strongly pseudoconvex domain has a contractive representation that is not completely contractive.

What are operator spaces ? Operator algebra group