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

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

1991-10-11

arxiv.org/abs/math/9201234v1

Mathematics

Functional Analysis

Scientific paper

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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