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arXiv · 1902.01735

Gleason parts for algebras of holomorphic functions on the ball of $\mathbf{c_0}$

Richard M. Aron·Verónica Dimant·Silvia Lassalle·Manuel Maestre
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Abstract

For a complex Banach space $X$ with open unit ball $B_X,$ consider the Banach algebras $\mathcal H^\infty(B_X)$ of bounded scalar-valued holomorphic functions and the subalgebra $\mathcal A_u(B_X)$ of uniformly continuous functions on $B_X.$ Denoting either algebra by $\mathcal A,$ we study the Gleason parts of the set of scalar-valued homomorphisms $\mathcal M(\mathcal A)$ on $\mathcal A.$ Following remarks on the general situation, we focus on the case $X = c_0.$

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Richard M. Aron, Verónica Dimant, Silvia Lassalle, Manuel Maestre. 2019-02-05. Gleason parts for algebras of holomorphic functions on the ball of $\mathbf{c_0}$. https://arxiv.org/abs/1902.01735

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