L¹ representation of Riesz spaces

Bahri Turan. "L¹ representation of Riesz spaces." Studia Mathematica 176.1 (2006): 61-68. <http://eudml.org/doc/284621>.

@article{BahriTuran2006,
abstract = {Let E be a Riesz space. By defining the spaces $L¹_\{E\}$ and $L_\{E\}^\{∞\}$ of E, we prove that the center $Z(L¹_\{E\})$ of $L¹_\{E\}$ is $L_\{E\}^\{∞\}$ and show that the injectivity of the Arens homomorphism m: Z(E)” → Z(E˜) is equivalent to the equality $L¹_\{E\} = Z(E)^\{\prime \}$. Finally, we also give some representation of an order continuous Banach lattice E with a weak unit and of the order dual E˜ of E in $L¹_\{E\}$ which are different from the representations appearing in the literature.},
author = {Bahri Turan},
journal = {Studia Mathematica},
keywords = {orthomorphism; ideal center; uniformly complete Riesz space; Banach lattice; -algebra; Arens homomorphism},
language = {eng},
number = {1},
pages = {61-68},
title = {L¹ representation of Riesz spaces},
url = {http://eudml.org/doc/284621},
volume = {176},
year = {2006},
}

TY - JOUR
AU - Bahri Turan
TI - L¹ representation of Riesz spaces
JO - Studia Mathematica
PY - 2006
VL - 176
IS - 1
SP - 61
EP - 68
AB - Let E be a Riesz space. By defining the spaces $L¹_{E}$ and $L_{E}^{∞}$ of E, we prove that the center $Z(L¹_{E})$ of $L¹_{E}$ is $L_{E}^{∞}$ and show that the injectivity of the Arens homomorphism m: Z(E)” → Z(E˜) is equivalent to the equality $L¹_{E} = Z(E)^{\prime }$. Finally, we also give some representation of an order continuous Banach lattice E with a weak unit and of the order dual E˜ of E in $L¹_{E}$ which are different from the representations appearing in the literature.
LA - eng
KW - orthomorphism; ideal center; uniformly complete Riesz space; Banach lattice; -algebra; Arens homomorphism
UR - http://eudml.org/doc/284621
ER -