Subspaces of $L_p$, p > 2, determined by partitions and weights

Dale E. Alspach, and Simei Tong. "Subspaces of $L_{p}$, p > 2, determined by partitions and weights." Studia Mathematica 159.2 (2003): 207-227. <http://eudml.org/doc/284403>.

@article{DaleE2003,
abstract = {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 $L_\{p\}$.},
author = {Dale E. Alspach, Simei Tong},
journal = {Studia Mathematica},
keywords = {complemented subspaces of ; norms given by partitions and weights; envelope norm},
language = {eng},
number = {2},
pages = {207-227},
title = {Subspaces of $L_\{p\}$, p > 2, determined by partitions and weights},
url = {http://eudml.org/doc/284403},
volume = {159},
year = {2003},
}

TY - JOUR
AU - Dale E. Alspach
AU - Simei Tong
TI - Subspaces of $L_{p}$, p > 2, determined by partitions and weights
JO - Studia Mathematica
PY - 2003
VL - 159
IS - 2
SP - 207
EP - 227
AB - 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 $L_{p}$.
LA - eng
KW - complemented subspaces of ; norms given by partitions and weights; envelope norm
UR - http://eudml.org/doc/284403
ER -