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.

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.

Sonic Geography, Place and Race in the Formation of Local Identity: Liverpool and Scousers

The concept of identity has attracted significant academic attention. This article unpacks what constitutes the Scouse identity, how it is constructed and its different dimensions, with particular reference to place, phonology and race. Its novelty lies in developing the underused concept of “sonic geography” to examine the extent to which sound, for example a distinctive accent and/or dialect, affects the construction of local identity. Empirically this is conducted through a detailed analysis of the Scouse, or Liverpudlian, identity. The article also deploys the concept of “sonic exclusion” to examine the role a distinguishing vernacular plays in shaping local identity and the extent to which it determines “who is in” and “who is out” as a Scouser. The conclusion is that an effective understanding of a Scouser is not only spatial – someone born in Liverpool – because the sonoric landscape of spoken Scouse, and thereby Scouse identity, extends beyond the contemporary political and geographic boundaries of the City of Liverpool.