Alexander Izzo

Adjunct Research Professor

Email: aizzo@bgsu.edu
Address: Department of Mathematics and Statistics
Bowling Green State University
Bowling Green, OH 43403-0206

Research Interests

• Banach algebras
  
• Functional analysis
  
• Function theory
• Several complex variables

Publications (since 2004)

A nontrivial uniform algebra Dirichlet on its maximal ideal space, arXiv:2403.19583

A sharper Swiss cheese, arXiv:2211.14684

A normal uniform algebra that fails to be strongly regular at a peak point, Pacific J. Math. 331 (2024), 77-97.

Polynomially convex sets whose union has nontrivial hull, Indiana U. Math. J. 73 (2024), 319-339.

Weak sequential completeness of uniform algebras (joint with Joel Feinstein), Irish Math. Soc. Bulletin 92 (2023), 27-32.

Polynomial hulls of arcs and curves II, Proc. Amer. Math. Soc. 151 (2023), 113-122.

One point Gleason parts and point derivations in uniform algebras (joint with Swarup Ghosh), Studia Math. 270 (2023), 323-337.

The set of bounded continuous nowhere locally uniformly continuous functions is not Borel, Houston J. Math. 48 (2022), 183-187.

Approximation by an algebra generated by holomorphic and conjugate holomorphic functions (joint with Timothy Clos), Rocky Mountain J. Math. 52 (2022), 1289-1294.

The Convergence of hulls of curves (joint with Edgar Lee Stout), Math. Zeit. 301 (2022), 3071-3086.

Polynomially convex arcs in polynomially convex simple closed curves. (joint with Edgar Lee Stout), Proc. Amer. Math. Soc. 150 (2022), 1591-1599.

Polynomial Hulls of Arcs and Curves, Proc. Amer. Math. Soc. 149 (2021), 199--207.

Gleason Parts and Point Derivations for Uniform Algebras with Dense Invertible Group II, Trans. Amer. Math. Soc. 374 (2021), 7105--7117.

Topology of Gleason Parts in Maximal Ideal Spaces with no Analytic Discs, (joint with Dimitris Papathanasiou), Canadian J. Math.   73 (2021), 177--194.

Spaces with Polynomial Hulls that Contain no Analytic Discs, Math. Ann.  378 (2020), 829--852.

A Doubly Generated Uniform Algebra with a One-Point Gleason Part off its Shilov Boundary, Studia Math. 252 (2020), 311--319.

No Topological Condition Implies Equality of Polynomial and Rational Hulls,
Proc. Amer. Math. Soc. 147 (2019), 5195-5207.

A Cantor Set whose Polynomial Hull Contains no Analytic Discs, (joint with Norman Levenberg),
Arkiv för Matem. 57 (2019), 373-379.

Analytic Discs and Uniform Algebras Generated by Real-analytic Functions,
Proc. Amer. Math. Soc. 147 (2019), 1519-1529.

A General Method for Constructing Essential Uniform Algebras, (joint with J. F. Feinstein),
Studia Math. 246 (2019), 47-61.

Hulls of Surfaces, (joint with Edgar Lee Stout),
Indiana Univ. Math. J. 67 (2018), 2061-2087.

A Hull with no Nontrivial Gleason Parts, (joint with Brian J. Cole and Swarup N. Ghosh),
Indiana Univ. Math. J. 67 (2018), 739-752.

Gleason Parts and Point Derivations for Uniform Algebras with Dense Invertible Group,
Trans. Amer. Math. Soc. 370 (2018), 4299-4321.

Pick and Peak Interpolation, Proc. Amer. Math. Soc. 146 (2018), 717-721.

Localization for Uniform Algebras Generated by Real-analytic Functions, (joint with John T. Anderson),
Proc. Amer. Math. Soc. 145 (2017), 4919-4930.

A Simple Proof of the Existence of Haar Measure on Amenable Groups,
Math. Scand. 120 (2017), 317-319.

Presence or Absence of Analytic Structure in Maximal Ideal Spaces,
(joint with Hakan Samuelsson Kalm and Erlend Fornaess Wold),
Math. Ann. 366 (2016), 459-478.

Existence of Continuous Functions that are One-to-one Almost Everywhere,
Math. Scand. 118 (2016), 269-276.

A Peak Point Theorem for Uniform Algebras on Real-analytic Varieties, (joint with John T. Anderson),
Math. Ann. 364 (2016), 657-665.

Uniform Algebras Invariant under Every Homeomorphism,
Trans. Amer. Math. Soc. 367 (2015), 231-250.

Generators for Algebras Dense in L^p-spaces (joint with Bo Li),
Studia Math. 217 (2013), 243-263.

Nonlocal Uniform Algebras on Three-Manifolds,
Pacific J. Math. 259 (2012), 109-116.

Uniform Approximation on Manifolds,
Annals of Math. 174 (2011), 55-73.

The Peak Point Conjecture and Uniform Algebras Invariant under Group Actions,
Contemp. Math. 547 (2011), 135-146.

Localization for Uniform Algebras Generated by Smooth Functions on Two-Manifolds,
Bull. London Math. Soc. 42 (2010), 652-660.

Uniform Algebras Invariant under Transitive Group Actions,
Indiana Univ. Math. J. 59 (2010), 417-426.

A Tetrachotomy for Certain Algebras Containing the Disc Algebra,
Proc. Amer. Math. Soc. 138 (2010), 623-627.

Uniform Algebras on the Sphere Invariant under Group Actions,
Math. Annalen 344 (2009), 989-995.

Peak Point Theorems for Uniform Algebras on Smooth Manifolds, (joint with John Anderson),
Math. Zeitschrift 261 (2009), 65-71.

Algebras Generated by the Disc Algebra and Bounded Harmonic Functions,
Proc. Amer. Math. Soc. 135 (2007), 1065-1071.

The Linear Span of Peak functions,
Proc. Edinburgh Math. Soc. 48 (2005), 631-634.

Some Algebras of Bounded Functions on the Disc,
Math. Reports Academy Sci. Canada 27 (2005), 72-75.

Algebras Generated by Holomorphic and Harmonic Functions on the Disc,
Bull. London Math. Soc. 37 (2005), 761-770.

Polynomial Approximation on Real-analytic Varieties in Cⁿ (joint with John Anderson and John Wermer),
Proc. Amer. Math. Soc. 132 (2004), 1495-1500.

Rational Approximation on the Unit Sphere in C² (joint with John Anderson and John Wermer),
Mich. Math. J. 52 (2004), 105-117.