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...

Full description

Saved in:

Bibliographic Details
Published in:	Journal of mathematical analysis and applications Vol. 542; no. 1; p. 128760
Main Author:	Popa, Dumitru
Format:	Journal Article
Language:	English
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
ISSN:	0022-247X
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
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