This article is cited in 3 papers

Brief communications

Perturbations of Strongly Continuous Operator Semigroups, and Matrix Muckenhoupt Weights

G. M. Gubreev^a, Yu. D. Latushkin<sup>b

a</sup> Poltava National Technical University named after Yuri Kondratyuk
^b University of Missouri-Columbia

Abstract: 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.

UDC: 517.98

Received: 09.03.2007

DOI: 10.4213/faa2916

 English version: Functional Analysis and Its Applications, 2008, 42:3, 234–238

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