: Mathematics: Banach algebra

mathematical analysis > functional analysis > Banach algebra

algebra > abstract algebra > algebraic structure > associative algebra > Banach algebra

Banach algebra

In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra ${\\displaystyle A}$ over the real or complex numbers (or over a non-Archimedean complete normed field) that at the same time is also a Banach space, that is, a normed space that is complete in the metric induced by the norm. The norm is required to satisfy over the real or complex numbers (or over a non-Archimedean complete normed field) that at the same time is also a Banach space, that is, a normed space that is complete in the metric induced by the norm. The norm is required to satisfy
${\\displaystyle \\|x\\,y\\|\\ \\leq \\|x\\|\\,\\|y\\|\\quad {\ ext{ for all }}x,y\\in A.}$
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Banach_algebra)

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