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Title: Unitary Banach algebras
Author: Cowell, S. R.
Awarding Body: University of Wales Swansea
Current Institution: Swansea University
Date of Award: 2003
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Chapter 1 defines the notion of a unitary Banach algebra, and gives various examples. The inheritance of the unitary property of quotients and subalgebras is investigated, the main result being that the class of unitary Banach algebras is exactly the class of quotients of discrete group algebras. One problem that is discussed is whether a unitary subalgebra needs to inherit the unit element. Chapter 2 gives several other characterisations of unitary Banach algebras among norm-unital Banach algebras, in particular by conditions on the numerical range. The topological properties of the unitary Banach algebra are also discussed. Chapter 3 deals with isometric isomorphisms of unitary Banach algebras. In particular it is shown that, for groups G1 and G2, and A a norm-unital Banach algebra with connected unitary group, or a unital C*-algebra, the existence of an isometric isomorphism from l1 (G1, A) onto ll (G2, A) implies that G1 and G2 are isomorphic. If A is commutative then these two results can be generalised to be case of locally compact abelian groups G1 and G2, and the Banach algebras L1(G1, A) and L1 (G2, A).
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available