Banach limit
id:
banach-limit-254-18594171
title:
Banach limit
text:
In mathematical analysis, a Banach limit is a continuous linear functional ϕ : ℓ ∞ → C :\ell ^{\infty }\to \mathbb {C} } defined on the Banach space ℓ ∞ of all bounded complex-valued sequences such that for all sequences x = , y = in ℓ ∞ , and complex numbers α : ϕ = α ϕ + ϕ (linearity);
if x n ≥ 0 for all n ∈ N , then ϕ ≥ 0 (positivity); ϕ = ϕ , where S is the shift operator defined by n = x n + 1 (shift-invariance);
if x is a convergent sequence, then ϕ = lim x . Hence, ϕ is an extension of t
brand slug:
wiki
category slug:
encyclopedia
description:
Mathematical term
original url:
https://en.wikipedia.org/wiki/Banach_limit
date created:
date modified:
2022-11-14T07:01:13Z
main entity:
{"identifier":"Q806060","url":"https://www.wikidata.org/entity/Q806060"}
image:
fields total:
13
integrity:
14