# Banach algebra

(redirected from Normed algebra)

## Banach algebra

[′bä‚näk ′al·jə·brə]
(mathematics)
An algebra which is a Banach space satisfying the property that for every pair of vectors, the norm of the product of those vectors does not exceed the product of their norms.

## Banach algebra

(mathematics)
An algebra in which the vector space is a Banach space.
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References in periodicals archive ?
n[member of]N] is an algebra sequence, then D(X,M) is a normed algebra.
Every unital (commutative or not) normed algebra (similarly, every unital p-normed algebra with p [member of] (0,1]) is a TQ-algebra, hence also a TQ-algebras (see [12], Proposition 2.
Let A be a normed algebra, [sigma] and [tau] two mappings on A and let M be an A-bimodule.
B] of A, generated by B, is a normed algebra with respect to the submultiplicative norm [parallel] x [parallel], defined by
Then (E, [tau]) is a complete locally m-convex algebra and (B, 0)-barrelled (namely, a barrelled one) and it is not a normed algebra.
Moreover, it is complete and barrelled, but neither unital or a normed algebra.
Given an internal normed algebra X, the finite part of Xis
mu]]) is a normed algebra with the norm [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.
But in any normed algebra, [beta] is less than or equal to the norm.
Participants of the July 2008 conference share recent research on affine transformation crossed product type algebras and noncommutative surfaces, C*-algebras associated with iterated function systems, extending representations of normed algebras in Banach spaces, and freeness of group actions on C*-algebras.
Feinstein, Completions of normed algebras of differentiable functions, Studia Math.
Duncan, Complete normed algebras, Springer-Verlag, Berlin, 1973.

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