Dissipative operators and operator Lipschitz functions
Copyright policy )Dissipative operators and operator Lipschitz functions
The purpose of this paper is to obtain an integral representation for the difference $f(L_1)-f(L_2)$ of functions of maximal dissipative operators. This representation in terms of double operator integrals will allow us to establish Lipschitz type estimates for functions of maximal dissipative operators. We also consider a similar problem for quasicommutators, i.e., operators of the form $f(L_1)R-Rf(L_2)$.
14 pages. arXiv admin note: text overlap with arXiv:1009.0298
- Michigan State University United States
- Steklov Mathematical Institute Russian Federation
- Department of Mathematical Sciences Russian Federation
- Friends University United States
- Peoples' Friendship University of Russia Russian Federation
Functional calculus for linear operators, 47A55, 47A60, 47A63, 47B44, Perturbation theory of linear operators, Mathematics - Complex Variables, Linear accretive operators, dissipative operators, etc., 530, 510, Functional Analysis (math.FA), Mathematics - Functional Analysis, Mathematics - Spectral Theory, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Linear operator inequalities, Complex Variables (math.CV), Spectral Theory (math.SP)
Functional calculus for linear operators, 47A55, 47A60, 47A63, 47B44, Perturbation theory of linear operators, Mathematics - Complex Variables, Linear accretive operators, dissipative operators, etc., 530, 510, Functional Analysis (math.FA), Mathematics - Functional Analysis, Mathematics - Spectral Theory, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Linear operator inequalities, Complex Variables (math.CV), Spectral Theory (math.SP)
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