Surjective isometries on a Banach space of analytic functions with bounded derivatives

2019/01/09 by Miura, Takeshi, Niwa, Norio
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1901.02737

Abstract

Let H(\mathbbD) be the linear space of all analytic functions on the open unit disc \mathbbD and H^p(\mathbbD) the Hardy space on \mathbbD. The characterization of complex linear isometries on S^p=\f∈ H(\mathbbD):f'∈ H^p(\mathbbD)\ was given for 1≤ p<∞ by Novinger and Oberlin in 1985. Here, we characterize surjective, not necessarily linear, isometries on S^∞.

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