Lie product type formulas for continuous multilinear operators

In this paper we prove various Lie product type formulas for continuous multilinear operators. A sample result: Let k≥2 be a natural number, X1,..., Xk, Y be Banach algebras with unit and T:X1×⋅⋅⋅×Xk→Y a continuous k-linear operator such that T(1,...,1)=1. Let also (an)n∈N be a sequence of natural n...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 542; no. 1; p. 128760
Main Author Popa, Dumitru
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.02.2025
Subjects
Banach algebra
Lie formulas for continuous multilinear operators
Matrix exponential
Lie formulas for continuous multilinear operators
Banach algebra
Matrix exponential
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Summary:In this paper we prove various Lie product type formulas for continuous multilinear operators. A sample result: Let k≥2 be a natural number, X1,..., Xk, Y be Banach algebras with unit and T:X1×⋅⋅⋅×Xk→Y a continuous k-linear operator such that T(1,...,1)=1. Let also (an)n∈N be a sequence of natural numbers such that limn→∞⁡an=∞. Then for all x1∈X1,..., xk∈Xk we havelimn→∞⁡[T(ex1an,...,exkan)]an=eT(x1,1,...,1)+T(1,x2,1,...,1)+⋅⋅⋅+T(1,...,1,xk).
ISSN:0022-247X
DOI:10.1016/j.jmaa.2024.128760