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 normal uniform algebra that fails to be strongly regular at a peak point, arXiv:2308.13951

A sharper Swiss cheese, arXiv:2211.14684

Weak sequential completeness of uniform algebras (joint with Joel Feinstein), Irish Math. Soc. Bulletin (accepted)

Polynomially convex sets whose union has nontrivial hull, Indiana Univ. Math. J. (accepted)

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

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

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.