Subspaces of $L_{p}$, p > 2, determined by partitions and weights

• Autorzy: Dale E. Alspach , Simei Tong
• Języki publikacji: EN

Abstrakty

EN

Many of the known complemented subspaces of $L_{p}$ have realizations as sequence spaces. In this paper a systematic approach to defining these spaces which uses partitions and weights is introduced. This approach gives a unified description of many well known complemented subspaces of $L_{p}$. It is proved that the class of spaces with such norms is stable under (p,2) sums. By introducing the notion of an envelope norm, we obtain a necessary condition for a Banach sequence space with norm given by partitions and weights to be isomorphic to a subspace of $L_{p}$. Using this we define a space Yₙ with norm given by partitions and weights with distance to any subspace of $L_{p}$ growing with n. This allows us to construct an example of a Banach space with norm given by partitions and weights which is not isomorphic to a subspace of $L_{p}$.

Kategorie tematyczne

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 159
• Numer: 2
• Strony: 207-227

Daty

wydano

2003

Twórcy

autor

Dale E. Alspach

• Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, U.S.A.

autor

Simei Tong

• Department of Mathematics, University of Wisconsin-Eau Claire, Eau Claire, WI 54702, U.S.A.

Identyfikatory

DOI

10.4064/sm159-2-4