Abstract
We study the similarity of perturbed compact operators to operators of block-diagonal structure with respect to some family of orthogonal projection operators, which allows us to refine and essentially strengthen results due to R. Turner. We obtain information about the operator realizing the similarity transformation, present estimates for the eigenvalues and eigenvectors of the perturbed operator, and also study the inverse problem of spectral analysis.
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REFERENCES
N. Dunford and J.T. Schwartz, Linear Operators,pt.3.Spectral Operators, Wiley, New York, 1971; Russian translation:Mir,Moscow,1974.
A.G. Baskakov, Harmonic Analysis of Linear Operators [in Russian ], Teaching aid,Izd.Voronezh Univ., Voronezh, 1987.
A. G. Baskakov, “Spectral analysis of perturbed nonquasianalytic nd spectral operators ”Izv.Ross. Akad.Nauk Ser.Mat. [Russian Acad.Sci.Izv.Math.], 58 (1994), no. 4, 3–32.
A. G. Baskakov, “Spectral analysis with respect to nite-dimensional perturbations of spectral operators,” Izv.Vyssh.Uchebn.Zaved.Mat. [Soviet Math.(Iz.VUZ )], (1991), no. 1, 3–11.
N. B. Uskova, “On the spectrum of di.erential operators of certain classes,”Differentsial 'nye Uravneniya [Di.erential Equations], 30 (1994), no. 2, 350–352.
A. G. Baskakov, “Estimates of the entries of inverse matrices and the spectral analysis of linear operators,” Izv.Ross.Akad.Nauk Ser.Mat. [Russian Acad.Sci.Izv.Math.], 61 (1997), no.6, 3–26.
N. B. Uskova, “On the estimates of spectral projections of perturbed self-adjoint operators,” Sibirsk. Mat.Zh. [Siberian Math.J.], 41 (2000), no.3, 712–721.
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Uskova, N.B. On a Result of R. Turner. Mathematical Notes 76, 844–854 (2004). https://doi.org/10.1023/B:MATN.0000049684.96209.3d
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DOI: https://doi.org/10.1023/B:MATN.0000049684.96209.3d