Operator Algebras with Unique Preduals

Operator Algebras with Unique Preduals

We show that every free semigroup algebras has a (strongly) unique Banach space predual. We also provide a new simpler proof that a weak-∗ closed unital operator operator algebra containing a weak-∗ dense subalgebra of compact operators has a unique Banach space predual.

Preduals of semigroup algebras

For a locally compact group G, the measure convolution algebra M(G) carries a natural coproduct. In previous work, we showed that the canonical predual C0(G) of M(G) is the unique predual which makes both the product and the coproduct on M(G) weak∗-continuous. Given a discrete semigroup S, the convolution algebra l(S) also carries a coproduct. In this paper we examine preduals for l(S) making b...

Effect algebras with state operator

Effect algebras have been introduced by Foulis and Bennett [2] (see also [3, 4] for equivalent definitions) for modeling unsharp measurements in quantum mechanical systems [5]. They are a generalization of many structures which arise in the axiomatization of quantum mechanics (Hilbert space effects [7]), noncommutative measure theory and probability (orthomodular lattices and posets, [6]), fuzz...

Operator Algebras

Notice that the left-hand side of the third equation is the sum of the left-hand sides of the first two. As a result, no solution to the system exists unless a + b = c. But if a + b = c, then any solution of the first two equations is also a solution of the third; and in any linear system involving more unknowns than equations, solutions, when they exist, are never unique. In the present case, ...

Operator Theory and Operator Algebras