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.
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.