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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Vydané v:	Journal of mathematical analysis and applications Ročník 542; číslo 1; s. 128760
Hlavný autor:	Popa, Dumitru
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier Inc 01.02.2025
Predmet:	Banach algebra Lie formulas for continuous multilinear operators Matrix exponential Lie formulas for continuous multilinear operators Banach algebra Matrix exponential
ISSN:	0022-247X
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Shrnutí:	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