Arens regularity and retractions
Glasgow mathematical journal, Tome 24 (1983) no. 1, pp. 17-21
Voir la notice de l'article provenant de la source Cambridge University Press
In this paper a characterisation of the regularity of a normed algebra A is given in terms of retractions onto A** from A4*. The second dual A** of a normed algebra A possesses two natural Banach algebra multiplications, say ° and *. Each of ° and * extends the original algebra multiplication on A; see (2). An algebra A is called regular if and only if F * G = F ° G for all F, G ∈ A**. See (1). The existing results in the Arens regularity theory can be found in a recent survey (2). Denoting the nth dual of A by An*, and en the natural embedding of An* in its second dual A(n+2)*, we can naturally represent the second dual A** of A as a Banach space retract of A4* in two different ways:Our main results say that A** is in fact a Banach algebra retract of A4* (i.e. the maps involved are homomorphisms) in either of these cases if and only if A is regular.
Arikan, Nilgün. Arens regularity and retractions. Glasgow mathematical journal, Tome 24 (1983) no. 1, pp. 17-21. doi: 10.1017/S0017089500005012
@article{10_1017_S0017089500005012,
author = {Arikan, Nilg\"un},
title = {Arens regularity and retractions},
journal = {Glasgow mathematical journal},
pages = {17--21},
year = {1983},
volume = {24},
number = {1},
doi = {10.1017/S0017089500005012},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500005012/}
}
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