THE ORDER BIDUAL OF ALMOST F-ALGEBRAS AND D-ALGEBRAS

Authors
BERNAU SJ HUIJSMANS CB
Citation
Sj. Bernau et Cb. Huijsmans, THE ORDER BIDUAL OF ALMOST F-ALGEBRAS AND D-ALGEBRAS, Transactions of the American Mathematical Society, 347(11), 1995, pp. 4259-4275
Citations number
14
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Transactions of the American Mathematical Society → ACNP
ISSN journal
00029947
Volume
347
Issue
11
Year of publication
1995
Pages
4259 - 4275
Database
ISI
SICI code
0002-9947(1995)347:11<4259:TOBOAF>2.0.ZU;2-P
Abstract
It is shown in this paper that the second order dual A'' of an Archime dean (almost) f-algebra A, equipped with the Arens multiplication, is again an (almost) S-algebra. Also, the order continuous bidual (A')'(n ) of an Archimedean d-algebra A is a d-algebra. Moreover, if the d-alg ebra A is commutative or has positive squares, then A'' is again a d-a lgebra.