Banach algebra


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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 ?
The norm on X and on B(X) the Banach algebra of all bounded linear operators acting on X, will be denoted by [parallel] * [paralle].
To be able to apply methods from the theory of Banach algebras to the solution of those problems, it is essential to determine if a class of linear operators of a sequence space X into itself is a Banach algebra; this is nontrivial if X is a BK space that does not have AK.
A painstakingly precise keeper of numbers - as a math prof, he wrote a two-volume, 1,617-page book on Banach algebra - Palmer has spreadsheets that shows he spent 8.
Let (X, [parallel]*[parallel]) be a Banach space and let B(X) be the Banach algebra of all linear and bounded operators acting from X into X.
Let B(H) denote the Banach algebra of all bounded linear operators on a Hilbert space H.
Every ([alpha], [phi])-approximate strongly higher derivation in a Banach algebra is a higher derivation.
2] is called a Banach algebra homomorphism if it is also multiplicative, i.
In [14], the present author investigated hypergeometric and basic hypergeometric series involving noncommutative parameters and argument (short: noncommutative hypergeometric series, and noncommutative basic or Q-hypergeometric series) over a unital ring R (or, when considering nonterminating series, over a unital Banach algebra R) from a different, nevertheless completely elementary, point of view.
Several of his appendices also offer independent interest, covering amenable groups, Banach algebra, bundles of C*-algebras, groups, representations of C*-algebras, direct integrals, Effros's ideal center decomposition, the Fell topology.
Additionally, in the papers just mentioned, the localization condition is generalized so that the cross-Gramian matrices of localized frames belong to a particular Banach algebra.
Among his topics are elements of measure theory, a Hilbert space interlude, linear transformations, locally convex spaces, and Banach algebras and spectral theory.