Extension and lifting of weakly continuous polynomials

• Autorzy: Raffaella Cilia , Joaquín M. Gutiérrez
• Języki publikacji: EN

Abstrakty

EN

We show that a Banach space X is an ℒ₁-space (respectively, an $ℒ_{∞}$-space) if and only if it has the lifting (respectively, the extension) property for polynomials which are weakly continuous on bounded sets. We also prove that X is an ℒ₁-space if and only if the space $𝓟_{wb}(^{m}X)$ of m-homogeneous scalar-valued polynomials on X which are weakly continuous on bounded sets is an $ℒ_{∞}$-space.

Kategorie tematyczne

• 46G25: (Spaces of) multilinear mappings, polynomials
• 46B20: Geometry and structure of normed linear spaces
• 47H60: Multilinear and polynomial operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 169
• Numer: 3
• Strony: 229-241

Daty

wydano

2005

Twórcy

autor

Raffaella Cilia

• Dipartimento di Matematica, Facoltà di Scienze, Università di Catania, Viale Andrea Doria 6, 95125 Catania, Italy

autor

Joaquín M. Gutiérrez

• Departamento de Matemática Aplicada, ETS de Ingenieros Industriales, Universidad Politécnica de Madrid, C. José Gutiérrez Abascal 2, 28006 Madrid, Spain

Identyfikatory

DOI

10.4064/sm169-3-2