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Distance Entre Puissances D'une Unité Approchée Bornée
Author(s) -
Berkani M.,
Esterle J.,
Mokhtari A.
Publication year - 2003
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702003927
Subject(s) - idempotence , bounded function , mathematics , banach algebra , identity (music) , unit (ring theory) , combinatorics , algebraic number , simple (philosophy) , algebra over a field , discrete mathematics , pure mathematics , physics , mathematical analysis , philosophy , mathematics education , epistemology , acoustics
Let A be a Banach algebra and let p and q be two positive integers. We show that if A has a left bounded sequential approximate identity (e n ) n⩾1 such that\slim, inf n →+∞|e p n‐e {p+q} n | ⩽ (p/p+q) p/q q/p+q} then A has a left‐bounded sequential identity (f n ) {n⩾1} such that f 2 n = f n for n⩾1. A simple example shows that the constant (p/p+q) p/q q/p+q is best possible. This result is based on some algebraic or integral formulae which associate an idempotent to elements of a Banach algebra satisfying some inequalities involving polynomials or entire functions.