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 ?
infinity]]-representation Banach algebra R(S) of a commutative topological semigroup S was introduced and extensively studied by Dunkl and Ramirez in [4].
By the middle of the summer of 1958 I finished writing my Diploma thesis: a theorem of decomposition of an anti-symmetric Banach algebra into a direct sum of two symmetric Banach algebras which Foias and myself proved.
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.
The Banach algebra of continuous functions on [bar.
Let A be a commutative Banach algebra without order.