Commutator conditions implying the convergence of the Lie–Trotter products

DOI10.1090/S0002-9939-01-06034-8zbMath0987.34061OpenAlexW1630561307MaRDI QIDQ2750852

Markus Wacker, Franziska Kühnemund

Publication date: 21 October 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-01-06034-8

zbMATH Keywords

strongly continuous semigroupsOrnstein-Uhlenbeck semigroupWeyl relationcommutator conditionsTrotter-Lie product formula

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Transformation and reduction of functional-differential equations and systems, normal forms (34K17) Linear differential equations in abstract spaces (34G10)

Related Items (3)

A simple counterexample related to the Lie-Trotter product formula ⋮ Dimension splitting for evolution equations ⋮ Sums and commutators of generators of noncommuting strongly continuous groups.

Cites Work

• On a functional analysis approach to parabolic equations in infinite dimensions
• On the Ornstein-Uhlenbeck operator in spaces of continuous functions
• The Lie-Trotter product formula does not hold for arbitrary sums of generators
• On the Product of Semi-Groups of Operators
• One-Parameter Semigroups for Linear Evolution Equations
• A theorem of the Dore-Venni type for noncommuting operators
• Product formulas, nonlinear semigroups, and addition of unbounded operators
• SOME RESULTS ON PARTIAL DIFFERENTIAL EQUATIONS AND ASIAN OPTIONS
• On the commutation relation $AB - BA = C$
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