Rademacher functions in Cesàro type spaces

• Autorzy: Sergei V. Astashkin , Lech Maligranda
• Języki publikacji: EN

Abstrakty

EN

The Rademacher sums are investigated in the Cesàro spaces $Ces_{p}$ (1 ≤ p ≤ ∞) and in the weighted Korenblyum-Kreĭn-Levin spaces $K_{p,w}$ on [0,1]. They span l₂ space in $Ces_{p}$ for any 1 ≤ p < ∞ and in $K_{p,w}$ if and only if the weight w is larger than $t log₂^{p/2}(2/t)$ on (0,1). Moreover, the span of the Rademachers is not complemented in $Ces_{p}$ for any 1 ≤ p < ∞ or in $K_{1,w}$ for any quasi-concave weight w. In the case when p > 1 and when w is such that the span of the Rademacher functions is isomorphic to l₂, this span is a complemented subspace in $K_{p,w}$.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46B42: Banach lattices

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 198
• Numer: 3
• Strony: 235-247

Daty

wydano

2010

Twórcy

autor

Sergei V. Astashkin

• Department of Mathematics and Mechanics, Samara State University, Akad. Pavlova 1, 443011 Samara, Russia

autor

Lech Maligranda

• Department of Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden

Identyfikatory

DOI

10.4064/sm198-3-3