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

Analytic disks in fibers over the unit ball of a Banach space.