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Displaying similar documents to “Banach spaces of functions analytic in a polydisc.”

A coding of separable Banach spaces. Analytic and coanalytic families of Banach spaces

Benoit Bossard (2002)

Fundamenta Mathematicae

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When the set of closed subspaces of C(Δ), where Δ is the Cantor set, is equipped with the standard Effros-Borel structure, the graph of the basic relations between Banach spaces (isomorphism, being isomorphic to a subspace, quotient, direct sum,...) is analytic non-Borel. Many natural families of Banach spaces (such as reflexive spaces, spaces not containing ℓ₁(ω),...) are coanalytic non-Borel. Some natural ranks (rank of embedding, Szlenk indices) are shown to be coanalytic ranks. Applications...

Intertwining Multiplication Operators on Function Spaces

Bahman Yousefi, Leila Bagheri (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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Suppose that X is a Banach space of analytic functions on a plane domain Ω. We characterize the operators T that intertwine with the multiplication operators acting on X.

A lower bound on the radius of analyticity of a power series in a real Banach space

Timothy Nguyen (2009)

Studia Mathematica

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Let F be a power series centered at the origin in a real Banach space with radius of uniform convergence ϱ. We show that F is analytic in the open ball B of radius ϱ/√e, and furthermore, the Taylor series of F about any point a ∈ B converges uniformly within every closed ball centered at a contained in B.