Geodesic
Perturbations of Strongly Continuous Operator Semigroups, and Matrix Muckenhoupt Weights
Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 3, pp. 85-89

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Let $A$ and $A_0$ be linear continuously invertible operators on a Hilbert space $\mathfrak{H}$ such that $A^{-1}-A_0^{-1}$ has finite rank. Assuming that $\sigma(A_0)=\varnothing$ and that the operator semigroup $V_+(t)=\exp\{iA_0t\}$, $t\ge0$, is of class $C_0$, we state criteria under which the semigroups $U_\pm(t)=\exp\{\pm iAt\}$, $t\ge0$, are of class $C_0$ as well. The analysis in the paper is based on functional models for nonself-adjoint operators and techniques of matrix Muckenhoupt weights.
Keywords: nonself-adjoint operator, perturbation of a semigroup, functional model, Muckenhoupt condition. 
@article{FAA_2008_42_3_a10,
     author = {G. M. Gubreev and Yu. D. Latushkin},
     title = {Perturbations of {Strongly} {Continuous} {Operator} {Semigroups,} and {Matrix} {Muckenhoupt} {Weights}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {85--89},
     publisher = {mathdoc},
     volume = {42},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2008_42_3_a10/}
}
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G. M. Gubreev; Yu. D. Latushkin. Perturbations of Strongly Continuous Operator Semigroups, and Matrix Muckenhoupt Weights. Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 3, pp. 85-89. http://geodesic.mathdoc.fr/item/FAA_2008_42_3_a10/