Functiones et Approximatio Commentarii Mathematici

Some problems concerning algebras of holomorphic functions

Richard M. Aron

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Let $X$ be a complex Banach space with open unit ball $B_X.$ We describe some recent work and a number of open problems related to the maximal ideal spaces of the Fréchet algebra of holomorphic functions of bounded type on $X$ and the Banach algebra of bounded holomorphic functions on $B_X$.

Article information

Funct. Approx. Comment. Math., Volume 59, Number 2 (2018), 269-277.

First available in Project Euclid: 28 March 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46J15: Banach algebras of differentiable or analytic functions, Hp-spaces [See also 30H10, 32A35, 32A37, 32A38, 42B30]
Secondary: 32A38: Algebras of holomorphic functions [See also 30H05, 46J10, 46J15] 42B30: $H^p$-spaces

maximal ideal space $\mathcal H^\infty(B_X)$ $\mathcal A_u(B_X)$ cluster value theorem


Aron, Richard M. Some problems concerning algebras of holomorphic functions. Funct. Approx. Comment. Math. 59 (2018), no. 2, 269--277. doi:10.7169/facm/1738.

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