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Representation of operators with martingales and the Radon-Nikodým property.

Manuel González, Antonio Martínez-Abejón, Javier Pello-García (2004)

Extracta Mathematicae

The Radon-Nikodým property was introduced to describe those Banach spaces X for which all operators acting between L1 and X have a representation function. These spaces can be characterized in terms of martingales, as those spaces in which every uniformly bounded martingale converges. In the present work we study some classes of operators defined upon their behaviour with respect to the convergence of such martingales. We prove that an operator preserves the non-convergence of uniformly bounded...

Rigidity of holomorphic isometries

Edoardo Vesentini (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A rigidity theorem for holomorphic families of holomorphic isometries acting on Cartan domains is proved.

Rigidity of holomorphic maps and distortion of biholomorphic maps in operator Siegel domains

Kazimierz Włodarczyk (1995)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Results concerning the rigidity of holomorphic maps and the distortion of biholomorphic maps in infinite dimensional Siegel domains of J * -algebras are established. The homogeneity of the open unit balls in these algebras plays a key role in the arguments.

Rings of PDE-preserving operators on nuclearly entire functions

Henrik Petersson (2004)

Studia Mathematica

Let E,F be Banach spaces where F = E’ or vice versa. If F has the approximation property, then the space of nuclearly entire functions of bounded type, ℋ N b ( E ) , and the space of exponential type functions, Exp(F), form a dual pair. The set of convolution operators on ℋ N b ( E ) (i.e. the continuous operators that commute with all translations) is formed by the transposes φ ( D ) ≡ t φ , φ ∈ Exp(F), of the multiplication operators φ :ψ ↦ φ ψ on Exp(F). A continuous operator T on ℋ N b ( E ) is PDE-preserving for a set ℙ ⊆ Exp(F) if it...

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.

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