TITLE

DISTANCE ENTRE PUISSANCES D'UNE UNIT APPROCHÃ‰E BORNÃ‰E

AUTHOR(S)
M. BERKANI; J. ESTERLE; A. MOKHTARI
PUB. DATE
April 2003
SOURCE
Journal of the London Mathematical Society;Apr2003, Vol. 67 Issue 2, p461
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
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 $(e_n)_{n\ge1}$ such that ${\rm lim}\,{\rm inf}_{n\to+\infty}\|e^p_n-e^{p+q}_n\| < ({p \over {p+q}})^{p\over q}{q\over{p+q}}$ then $A$ has a left-bounded sequential identity $(f_n)_{n\ge1}$ such that $f^2_n = f_n$ for $n\ge1$. A simple example shows that the constant $({p\over {p+q}})^{p\over q}{q\over{p+q}}$ 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.
ACCESSION #
11992973

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