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Commutators and analytic families of operators

Published online by Cambridge University Press:  14 November 2011

María J. Carro
María J. Carro
Affiliation:
Departament de Matemàtic Aplicada i Anàlisi, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain (carro@mat.ub.es)
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Extract

This work connects the theory of commutators with analytic families of operators in abstract interpolation theory. Our main result asserts that if {Lξ}0≤Reξ≤1 is an analytic family of operators satisfying some conditions, then [Lθ,Ω] +(Lξ)′(θ): Āθ→ Bθ is bounded. From this, we can deduce the boundedness of the commutator .

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 129 , Issue 4 , 1999 , pp. 685 - 696
Copyright
Copyright © Royal Society of Edinburgh 1999

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