The order bidual of f -algebras revisited

Boulabiar, Karim; Jaber, Jamel

doi:10.1007/s11117-010-0072-x

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Preliminaries1

Proof the Norm Completion A Of A Is A Unital Closed Subalge1

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Cited by 4 publications

(2 citation statements)

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“…the Arens multiplication [4]. In the literature, there are several studies, for example [5][6][7]9], that respond the…”

Section: Preliminariesmentioning

confidence: 99%

Pre-Markov operators

Duru¹,

Ilter²

2020

Turk J Math

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In Operator Theory characterizing extreme points has been systematically studied in a convex set of linear operators from an algebra to another. This paper presents some new characterizations. We define pre-Markov operators and identify when the second adjoint of a linear positive operator being an extreme point in the collection of all Markov operators between the unital second order duals of two unital f-algebras. Moreover a characterization of extreme points is given in the collection of all contractive operators between unital f-algebras. In addition, we give a condition that makes an order bounded algebra homomorphism is a lattice homomorphism.

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“…the Arens multiplication [4]. In the literature, there are several studies, for example [5][6][7]9], that respond the…”

Section: Preliminariesmentioning

confidence: 99%

Pre-Markov operators

Duru¹,

Ilter²

2020

Turk J Math

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show abstract

“…Remark 1. Characterizations of f -algebras A such that (A ∼ ) ∼ n has unit are given in [8], [4], [10]. Related to Corollary 3 , we mention that we do not know any examples of semi-prime f -algebras that do not have topologically full center.…”

Section: Proof the Norm Completion A Of A Is A Unital Closed Subalgementioning

confidence: 99%

Characterization of Riesz Spaces with Topologically Full Center

Alpay

Orhon

2016

Trends in Mathematics

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Abstract. Let E be a Riesz space and let E ∼ denote its order dual. The orthomorphisms Orth(E) on E, and the ideal center Z(E) of E, are naturally embedded in Orth(E ∼ ) and Z(E ∼ ) respectively. We construct two unital algebra and order continuous Riesz homomorphismsandthat extend the above mentioned natural inclusions respectively. Then, the range of γ is an order ideal in Orth(E ∼ ) if and only if m is surjective. Furthermore, m is surjective if and only if E has a topologically full center. (That is, the σ(E, E ∼ )-closure of Z(E)x contains the order ideal generated by x for each x ∈ E+.) As a consequence, E has a topologically full center Z(E) if and only if Z(E ∼ ) = π · Z(E) ′′ for some idempotent π ∈ Z(E)′′ .

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$$f$$ -algebras with a $$\sigma $$ -bounded approximate unit

Jaber

2013

Positivity

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The order bidual of f -algebras revisited

Abstract: It is shown that the order bidual X ∼∼ of an Archimedean semiprime f -algebra X has a unit element for the Arens multiplication if and only if every positive linear functional on X extends to a positive linear functional on the f -algebra Orth (X ) of all orthomorphisms on X .

Cited by 4 publications

References 7 publications

Pre-Markov operators

Pre-Markov operators

Characterization of Riesz Spaces with Topologically Full Center

$$f$$ -algebras with a $$\sigma $$ -bounded approximate unit

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