On Projective Limits of Real C * -and Jordan Operator Algebras 1
نویسندگان
چکیده
Projective limits of Banach algebras have been studied sporadically by many authors since 1952, when they were first introduced by Arens [2] and Michael [11]. Projective limits of complex C∗-algebras were first mentioned by Arens [2]. They have since been studied under various names by Wenjen [20], Sya Do-Shin [18], Brooks [4], Inoue [10], Schmüdgen [17], Fritzsche [6–7], Fragoulopoulou [5], Phillips [15], etc. We will follow Inoue [10] in the usage of the name «locally C ∗-algebras» for these objects. At the same time, in parallel with the theory of complex C∗-algebras, a theory of their real and Jordan analogues, namely real C∗-algebras and JB-algebras, has been actively developed by various authors (for references, see for example [3, 8, 12]). In the view of aforementioned, it is therefore interesting to extend existing theory to the case of real and Jordan analogues of complex locally C∗-algebras. The present paper (first in a sequence under preparation) is devoted to definitions and basic properties of such analogues, which we call real locally C∗and locally JB-algebras.
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