Banach algebra

In functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers which at the same time is also a Banach space. The algebra multiplication and the Banach space norm are required to be related by the following inequality:

Related Topics:
Functional analysis - Stefan Banach - Associative algebra - Real - Complex - Banach space

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: orall x, y in A , |x , y| leq |x | , | y|

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(i.e., the norm of the product is less than or equal to the product of the norms.)

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This ensures that the multiplication operation is continuous.

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A Banach algebra is called "unital" if it has an identity element for the multiplication whose norm is 1, and "commutative" if its multiplication is commutative.

Related Topics:
Identity element - Commutative

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Banach algebras can also be defined over fields of p-adic numbers. This is part of p-adic analysis.

Related Topics:
P-adic number - P-adic analysis

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