L¹ representation of Riesz spaces
Bahri Turan
Studia Mathematica, Tome 173 (2006), p. 61-68 / Harvested from The Polish Digital Mathematics Library
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Let E be a Riesz space. By defining the spaces L¹E and LE∞ of E, we prove that the center Z(L¹E) of L¹E is LE∞ and show that the injectivity of the Arens homomorphism m: Z(E)” → Z(E˜) is equivalent to the equality L¹E=Z(E)'. 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 L¹E which are different from the representations appearing in the literature.

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:284621 
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     title = {L$^1$ representation of Riesz spaces},
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     year = {2006},
     pages = {61-68},
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     language = {en},
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Bahri Turan. L¹ representation of Riesz spaces. Studia Mathematica, Tome 173 (2006) pp. 61-68. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm176-1-4/