B. J. Cole, T. W. Gamelin, William B. Johnson
Published 1991-10-11Version 1
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.
Some inequalities for $(α, β)$-normal operators in Hilbert spaces
Avoiding σ-porous sets in Hilbert spaces
The splitting lemmas for nonsmooth functionals on Hilbert spaces I
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