A stably unital local Banach algebra 
is one for which 
has an approximate
identity consisting of idempotents (Blackadar
1998, p. 31). Here 
is the algebraic direct limit of the matrix algebras 
under the embeddings 
, equivalently the infinite
matrices with only finitely many nonzero
entries (Blackadar 1998, p. 27).
Stably Unital
See also
Algebra, Analytic Function, Approximate Identity, Banach Algebra, Completion, Involution, Local Banach Algebra, Normed Space, Positive Element, Subalgebra, UnitalPortions of this entry contributed by Christopher Stover
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References
Blackadar, B. K-Theory for Operator Algebras, 2nd ed. New York: Cambridge University Press, 1998.Referenced on Wolfram|Alpha
Stably UnitalCite this as:
Weisstein, Eric W., with contributions by Christopher Stover. "Stably Unital." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StablyUnital.html