Some remarks on quasi-Cohen sets

• Autorzy: Pascal Lefèvre , Daniel Li
• Języki publikacji: EN

Abstrakty

EN

We are interested in Banach space geometry characterizations of quasi-Cohen sets. For example, it turns out that they are exactly the subsets E of the dual of an abelian compact group G such that the canonical injection $C(G)/C_{E^{c}}(G) ↪ L²_{E}(G)$ is a 2-summing operator. This easily yields an extension of a result due to S. Kwapień and A. Pełczyński. We also investigate some properties of translation invariant quotients of L¹ which are isomorphic to subspaces of L¹.

Kategorie tematyczne

• 42A55: Lacunary series of trigonometric and other functions; Riesz products
• 42A20: Convergence and absolute convergence of Fourier and trigonometric series
• 43A77: Analysis on general compact groups
• 43A46: Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
• 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2001
• Tom: 89
• Numer: 2
• Strony: 169-178

Daty

wydano

2001

Twórcy

autor

Pascal Lefèvre

• Faculté Jean Perrin, Université d'Artois, rue Jean Souvraz S.P. 18, 62307 Lens Cedex, France

autor

Daniel Li

• Faculté Jean Perrin, Université d'Artois, rue Jean Souvraz S.P. 18, 62307 Lens Cedex

Identyfikatory

DOI

10.4064/cm89-2-2