L¹ representation of Riesz spaces

• Autorzy: Bahri Turan
• Języki publikacji: EN

Abstrakty

EN

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 $L¹_{E} = Z(E)'$. 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.

Kategorie tematyczne

• 46A40: Ordered topological linear spaces, vector lattices
• 47B65: Positive operators and order-bounded operators
• 47B60: Operators on ordered spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 176
• Numer: 1
• Strony: 61-68

Daty

wydano

2006

Twórcy

autor

Bahri Turan

• Department of Mathematics, Faculty of Arts and Science, Gazi University, Teknikokullar, 06500 Ankara, Turkey

Identyfikatory

DOI

10.4064/sm176-1-4