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Disclaimer: This dissertation does not contain plagiarised material; except where otherwise stated all theorems are the author's. Acknowledgement: Many thanks to Joel Feinstein for guidance with the literature, useful suggestions and comments on this work.

- William J. Bland, Joel F. Feinstein
- 2003

In this paper we look at normed spaces of differentiable functions on compact plane sets, including the spaces of infinitely differentiable functions considered by Dales and Davie in [7]. For many compact plane sets the classical definitions give rise to incomplete spaces. We introduce an alternative definition of differentiability which allows us to… (More)

- Richard M Braun, David C Sahadevan, Joel Feinstein
- Techniques in hand & upper extremity surgery
- 2006

Scalene muscle block is often performed to assist with the clinical differentiation of primary sources of pain and weakness in the upper limb when the differential diagnosis includes thoracic outlet syndrome. This presentation offers a simple clinical method to assess needle placement in the scalene muscle before an injection of local anesthetic which, if… (More)

Let (M n) be a sequence of positive numbers satisfying M 0 = 1 and M n+m

This note is a sequel to [7] where we investigated the endomorphisms of a certain class of Banach algebras of infinitely differentiable functions on the unit interval. Start with a perfect, compact plane set X. We say that a complex-valued function f defined on X is complex-differentiable at a point a ∈ X if the limit f ′ (a) = lim z→a, z∈X f (z) − f (a) z… (More)

A survey is given of the work on strong regularity for uniform algebras over the last thirty years, and some new results are proved, including the following. Let A be a uniform algebra on a compact space X and let E be the set of all those points x ∈ X such that A is not strongly regular at x. If E has no non-empty, perfect subsets then A is normal, and X… (More)

Let A be a unital Banach function algebra with character space Φ A. For x ∈ Φ A , let M x and J x be the ideals of functions vanishing at x, and in a neighbourhood of x, respectively. It is shown that the hull of J x is connected, and that if x does not belong to the Shilov boundary of A then the set {y ∈ Φ A : M x ⊇ J y } has an infinite, connected subset.… (More)

This paper continues the study of spectral synthesis and the topologies τ ∞ and τ r on the ideal space of a Banach algebra, concentrating particularly on the class of Haagerup tensor products of C *-algebras. For this class, it is shown that spectral synthesis is equivalent to the Hausdorffness of τ ∞. Under a weak extra condition, spectral synthesis is… (More)

- T W Dawson, J F Feinstein
- 2008

We examine the condition that a complex Banach algebra A have dense invertible group. We show that, for commutative algebras, this property is preserved by integral extensions. We also investigate the connections with an old problem in the theory of uniform algebras.

- J F Feinstein
- 2000

In this note we construct Swiss cheeses X such that R(X) is non-regular but such that R(X) has no non-trivial Jensen measures. We also construct a non-regular uniform algebra with compact, metrizable character space such that every point of the character space is a peak point. In [Co] Cole gave a counterexample to the peak point conjecture by constructing a… (More)