Banach algebra

In mathematics, especially 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: (i.e., the norm of the product is less than or equal to the product of the norms.) This ensures that the multiplication operation is continuous.
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<mathematics> An algebra in which the vector space is a Banach space.
(1997-02-25)