Functional Analysis and Its Applications

, Volume 50, Issue 2, pp 143–145 | Cite as

An algebra of continuous functions as a continuous envelope of its subalgebras

  • S. S. Akbarov
Brief Communications


To an arbitrary involutive stereotype algebra A the continuous envelope operation assigns its nearest, in some sense, involutive stereotype algebra EnvC A so that homomorphisms to various C*-algebras separate the elements of Env C A but do not distinguish between the properties of A and those of Env C A.

If A is an involutive stereotype subalgebra in the algebra C(M) of continuous functions on a paracompact locally compact topological space M, then, for C(M) to be a continuous envelope of A, i.e., Env C A = C(M), it is necessary but not sufficient that A be dense in C(M). In this note we announce a necessary and sufficient condition for this: the involutive spectrum of A must coincide with M up to a weakening of the topology such that the system of compact subsets in M and the topology on each compact subset remains the same.

Key words

C*-algebra stereotype algebra 


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Moscow Aviation InstituteMoscowRussia

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