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Schauder bases and the bounded approximation property in separable Banach spaces

Jorge Mujica, Daniela M. Vieira (2010)

Studia Mathematica

Let E be a separable Banach space with the λ-bounded approximation property. We show that for each ϵ > 0 there is a Banach space F with a Schauder basis such that E is isometrically isomorphic to a 1-complemented subspace of F and, moreover, the sequence (Tₙ) of canonical projections in F has the properties s u p n ∈ ℕ | | T ₙ | | ≤ λ + ϵ and l i m s u p n → ∞ | | T ₙ | | ≤ λ . This is a sharp quantitative version of a classical result obtained independently by Pełczyński and by Johnson, Rosenthal and Zippin.

Separable quotients of Banach spaces.

Jorge Mújica (1997)

Revista Matemática de la Universidad Complutense de Madrid

In this survey we show that the separable quotient problem for Banach spaces is equivalent to several other problems for Banach space theory. We give also several partial solutions to the problem.

Separating polynomials on Banach spaces.

R. Gonzalo, J. A. Jaramillo (1997)

Extracta Mathematicae

In this paper we survey some recent results concerning separating polynomials on real Banach spaces. By this we mean a polynomial which separates the origin from the unit sphere of the space, thus providing an analog of the separating quadratic form on Hilbert space.

Shilov boundary for holomorphic functions on some classical Banach spaces

María D. Acosta, Mary Lilian Lourenço (2007)

Studia Mathematica

Let ∞ ( B X ) be the Banach space of all bounded and continuous functions on the closed unit ball B X of a complex Banach space X and holomorphic on the open unit ball, with sup norm, and let u ( B X ) be the subspace of ∞ ( B X ) of those functions which are uniformly continuous on B X . A subset B ⊂ B X is a boundary for ∞ ( B X ) if ∥ f ∥ = s u p x ∈ B | f ( x ) | for every f ∈ ∞ ( B X ) . We prove that for X = d(w,1) (the Lorentz sequence space) and X = C₁(H), the trace class operators, there is a minimal closed boundary for ∞ ( B X ) . On the other hand, for X = , the Schreier space,...

Surjective factorization of holomorphic mappings

Manuel Gonzalez, Joaquín M. Gutiérrez (2000)

Commentationes Mathematicae Universitatis Carolinae

We characterize the holomorphic mappings f between complex Banach spaces that may be written in the form f = T ∘ g , where g is another holomorphic mapping and T belongs to a closed surjective operator ideal.

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