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Banach spaces of homogeneous polynomials without the approximation property

Seán Dineen, Jorge Mujica (2015)

Czechoslovak Mathematical Journal

We present simple proofs that spaces of homogeneous polynomials on L p [ 0 , 1 ] and p provide plenty of natural examples of Banach spaces without the approximation property. By giving necessary and sufficient conditions, our results bring to completion, at least for an important collection of Banach spaces, a circle of results begun in 1976 by R. Aron and M. Schottenloher (1976).

Banach-valued axiomatic spectra

S. Seán, Robin E. Harte (2006)

Studia Mathematica

Using axiomatic joint spectra we obtain a functional calculus which extends our previous Gelfand-Waelbroeck type results to include a Banach-valued Taylor-Waelbroeck spectrum.

Bounded analytic sets in Banach spaces

Volker Aurich (1986)

Annales de l'institut Fourier

Conditions are given which enable or disable a complex space X to be mapped biholomorphically onto a bounded closed analytic subset of a Banach space. They involve on the one hand the Radon-Nikodym property and on the other hand the completeness of the Caratheodory metric of X .

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