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Analytic Disks in Fibers over the Unit Ball of a Banach Space

B. J. Cole·T. W. Gamelin·William B. Johnson
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Abstract

We study biorthogonal sequences with special properties, such as weak or weak-star convergence to 0, and obtain an extension of the Josefson-Nissenzweig theorem. This result is applied to embed analytic disks in the fiber over 0 of the spectrum of H^infinity (B), the algebra of bounded analytic functions on the unit ball B of an arbitrary infinite dimensional Banach space. Various other embedding theorems are obtained. For instance, if the Banach space is superreflexive, then the unit ball of a Hilbert space of uncountable dimension can be embedded analytically in the fiber over 0 via an embedding which is uniformly bicontinuous with respect to the Gleason metric.

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BibTeXRIS

B. J. Cole, T. W. Gamelin, William B. Johnson. 1991-10-11. Analytic Disks in Fibers over the Unit Ball of a Banach Space. https://arxiv.org/abs/math/9201234

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