Maximal C*-algebras of quotients and injective envelopes of C*-algebras

A new C*-enlargement of a C*-algebra A nested between the local multiplier algebra of A and its injective envelope is introduced. Various aspects of this maximal C*-algebra of quotients are studied, notably in the setting of AW*-algebras. As a by-product we obtain a new example of a type I C*-algebra such that its second iterated local multiplier algebra is strictly larger than its local multiplier algebra.

Sheaves of C*-algebras

We develop the basics of a theory of sheaves of C*-algebras and, in particular, compare it to the existing theory of C*-bundles. The details of two fundamental examples, the local multiplier sheaf and the injective envelope sheaf, are discussed.

The suppression of q card selections: Evidence for deductive inference in Wason's Selection Task

The results of three experiments investigating the role of deductive inference in Wason's selection task are reported. In Experiment 1, participants received either a standard one-rule problem or a task containing a second rule, which specified an alternative antecedent. Both groups of participants were asked to select those cards that they considered were necessary to test whether the rule common to both problems was true or false. The results showed a significant suppression of q card selections in the two-rule condition. In addition there was weak evidence for both decreased p selection and increased not-q selection. In Experiment 2 we again manipulated number of rules and found suppression of q card selections only. Finally, in Experiment 3 we compared one- and two-rule conditions with a two-rule condition where the second rule specified two alternative antecedents in the form of a disjunction. The q card selections were suppressed in both of the two-rule conditions but there was no effect of whether the second rule contained one or two alternative antecedents. We argue that our results support the claim that people make inferences about the unseen side of the cards when engaging with the indicative selection task.

Bimodules over nest algebras and Deddens'

We generalise Dedden's Theorem for nest algebras to nest algebra bimodules. We define an object which extends the Jacobson radical of a nest algebra, and characterose it generalising a theorem of Erdos.

Jordan isomorphism of purely infinite C*-algebras

We prove that every unital bounded linear mapping from a unital purely infinite C*-algebra of real rank zero into a unital Banach algebra which preserves elements of square zero is a Jordan homomorphism. This entails a description of unital surjective spectral isometries as the Jordan isomorphisms in this setting.

Cohomology of Banach algebras of operators and geometry of Banach spaces.

In the paper we give an exposition of the major results concerning the relation between first order cohomology of Banach algebras of operators on a Banach space with coefficients in specified modules and the geometry of the underlying Banach space. In particular we shall compare the properties weak amenability and amenability for Banach algebras A(X), the approximable operators on a Banach space X. Whereas amenability is a local property of the Banach space X, weak amenability is often the consequence of properties of large scale geometry.

Amenability of algebras of approximable operators

We give a necessary and sufficient condition for amenability of the Banach algebra of approximable operators on a Banach space. We further investigate the relationship between amenability of this algebra and factorization of operators, strengthening known results and developing new techniques to determine whether or not a given Banach space carries an amenable algebra of approximable operators. Using these techniques, we are able to show, among other things, the non-amenability of the algebra of approximable operators on Tsirelson’s space.