Gleason parts for algebras of holomorphic functions on the ball of c₀

2019/02/05 by Aron, Richard M., Dimant, Verónica, Lassalle, Silvia +1
#30H05 #30H50 #46E50 #46J15 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1902.01735

Abstract

For a complex Banach space X with open unit ball B_X, consider the Banach algebras \mathcal H^∞(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 = c₀.

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