All Outputs (15)

Weak Sequential Completeness of Uniform Algebras (2024)
Journal Article
Feinstein, J. F., & Izzo, A. J. (2024). Weak Sequential Completeness of Uniform Algebras. Bulletin of the Irish Mathematical Society, 92(Winter), 27-32. https://doi.org/10.33232/bims.0092.27.32

We give a simple, elementary proof that a uniform algebra is weakly sequentially complete if and only if it is finite-dimensional.

Factorization in commutative Banach algebras (2021)
Journal Article
Dales, H. G., Feinstein, J. F., & Pham, H. L. (2021). Factorization in commutative Banach algebras. Studia Mathematica, 259, 79-120. https://doi.org/10.4064/sm191216-22-7

Let A be a (non-unital) commutative Banach algebra. We consider when A has a variety of factorization properties: we list the (ob-vious) implications between these properties, and then consider whether any of these implications can be reversed in var... Read More about Factorization in commutative Banach algebras.

Regularity of R(X) does not pass to finite unions (2020)
Journal Article
Feinstein, J. F. (2020). Regularity of R(X) does not pass to finite unions. Proceedings of the American Mathematical Society, 148(7), 2931-2936. https://doi.org/10.1090/proc/14944

We show that there are compact plane sets X, Y such that R(X) and R(Y) are regular but R(X ∪ Y) is not regular.

A general method for constructing essential uniform algebras (2018)
Journal Article
Feinstein, J., & Izzo, A. J. (2019). A general method for constructing essential uniform algebras. Studia Mathematica, 246, 47-61. https://doi.org/10.4064/sm170907-23-2

A general method for constructing essential uniform algebras with prescribed properties is presented. Using the method, the following examples are constructed: an essential, natural, regular uniform algebra on the closed unit disc; an essential, natu... Read More about A general method for constructing essential uniform algebras.

Quasianalyticity in certain Banach function algebras (2017)
Journal Article
Feinstein, J., & Morley, S. (in press). Quasianalyticity in certain Banach function algebras. Studia Mathematica, 238(2), https://doi.org/10.4064/sm8614-12-2016

Let X be a perfect, compact subset of the complex plane. We consider algebras of those functions on X which satisfy a generalized notion of differentiability, which we call F-differentiability. In particular, we investigate a notion of quasianalytici... Read More about Quasianalyticity in certain Banach function algebras.

Regularity points and Jensen measures for R(X) (2016)
Journal Article
Feinstein, J., & Yang, H. (in press). Regularity points and Jensen measures for R(X). Studia Mathematica, 235(1), https://doi.org/10.4064/sm8351-7-2016

We discuss two types of `regularity point', points of continuity and R-points for Banach function algebras, which were introduced by the first author and Somerset in (2000). We show that, even for the natural uniform algebras R(X) (for compact plane... Read More about Regularity points and Jensen measures for R(X).

The chain rule for F-differentiation (2016)
Journal Article
Chaobankoh, T., Feinstein, J., & Morley, S. (2016). The chain rule for F-differentiation

Let X be a perfect, compact subset of the complex plane, and let D (1)(X) denote the (complex) algebra of continuously complex-differentiable functions on X. Then D(1)(X) is a normed algebra of functions but, in some cases, fails to be a Banach funct... Read More about The chain rule for F-differentiation.

Abstract Swiss cheese space and classicalisation of Swiss cheeses (2016)
Journal Article
Feinstein, J., Morley, S., & Yang, H. (2016). Abstract Swiss cheese space and classicalisation of Swiss cheeses. Journal of Mathematical Analysis and Applications, 438(1), 119-141. https://doi.org/10.1016/j.jmaa.2016.02.004

Swiss cheese sets are compact subsets of the complex plane obtained by deleting a sequence of open disks from a closed disk. Such sets have provided numerous counterexamples in the theory of uniform algebras. In this paper, we introduce a topological... Read More about Abstract Swiss cheese space and classicalisation of Swiss cheeses.

Removability of exceptional sets for differentiable and Lipschitz functions (2015)
Journal Article
Craig, J., Feinstein, J., & Patrick, P. (2015). Removability of exceptional sets for differentiable and Lipschitz functions. 00 Journal not listed, 645, https://doi.org/10.1090/conm/645

We discuss removability problems concerning differentiability and pointwise Lipschitz conditions for functions of a real variable. We prove that, in each of the settings under consideration, a set is removable if and only if it has no perfect subsets... Read More about Removability of exceptional sets for differentiable and Lipschitz functions.

Partial regularity and t-analytic sets for Banach function algebras (2011)
Journal Article
Feinstein, J., & Mortini, R. (2012). Partial regularity and t-analytic sets for Banach function algebras. Mathematische Zeitschrift, 271(1-2), https://doi.org/10.1007/s00209-011-0856-0

In this note we introduce the notion of t-analytic sets. Using this concept, we construct a class of closed prime ideals in Banach function algebras and discuss some problems related to Alling’s conjecture in H infinity. A description of all closed t... Read More about Partial regularity and t-analytic sets for Banach function algebras.

Normed algebras of differentiable functions on compact plane sets (2010)
Journal Article
Dales, H., & Feinstein, J. (2010). Normed algebras of differentiable functions on compact plane sets. Indian Journal of Pure and Applied Mathematics, 41(1), https://doi.org/10.1007/s13226-010-0005-1

We investigate the completeness and completions of the normed algebras (D(1)(X),∥•∥) for perfect, compact plane sets X. In particular, we construct a radially self-absorbing, compact plane set X such that the normed algebra (D(1)(X),∥•∥) is not compl... Read More about Normed algebras of differentiable functions on compact plane sets.

Spectral synthesis and topologies on ideal spaces for Banach *-algebras (2002)
Journal Article
Feinstein, J., Kaniuth, E., & Somerset, D. (2002). Spectral synthesis and topologies on ideal spaces for Banach *-algebras. Journal of Functional Analysis, 196(1), https://doi.org/10.1006/jfan.2002.3964

This paper continues the study of spectral synthesis and the topologies ?? and ?r on the ideal space of a Banach algebra, concentrating on the class of Banach *-algebras, and in particular on L1-group algebras. It is shown that if a group G is a fini... Read More about Spectral synthesis and topologies on ideal spaces for Banach *-algebras.

Trivial Jensen measures without regularity
Journal Article
Feinstein, J. (1999). Trivial Jensen measures without regularity

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 chara... Read More about Trivial Jensen measures without regularity.

Endomorphisms of Banach algebras of infinitely differentiable functions
Journal Article
Feinstein, J., & Kamowitz, H. (1999). Endomorphisms of Banach algebras of infinitely differentiable functions

In this note we study the endomorphisms of certain Banach algebras of infinitely differentiable functions on compact plane sets, associated with weight sequences M. These algebras were originally studied by Dales, Davie and McClure. In a pr... Read More about Endomorphisms of Banach algebras of infinitely differentiable functions.

Spectral synthesis for Banach Algebras II
Journal Article
Feinstein, J., & Somerset, D. (1999). Spectral synthesis for Banach Algebras II

This paper continues the study of spectral synthesis and the topologies tau-infinity and tau-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 tha... Read More about Spectral synthesis for Banach Algebras II.