Ukrainian Mathematical Bulletin

Volume 3, Issue 4, 2006 pp. 447-483.

Operator Pencils of the Second Order and Linear Fractional Relations

Authors: Victor Khatskevich, Irina I. Karelin, Leonid Zelenko
Author institution: Victor Khatskevich, Department of Mathematics ORT Braude Academic College, College Campus, P.O.Box 78, Karmiel, 21982, Israel, victor_kh@hotmail.com Irina I.Karelin, Lincoln str. 2/3, Haifa, Israel, 34369, Irina@generic-imaging.com Leonid Zelenko, Department of Mathematics, University of Haifa, 31905 Haifa, Israel, zelenko@math.haifa.ac.il

Summary: The notions of a pencil of the second order and a linear fractional relation (LFR) are defined in spaces of linear bounded operators acting between Banach spaces. It is shown that these notions are closely connected with various theoretical and applied problems and have diverse applications. A number of the open problems, both for pencils and LFR, are posed in this paper. Some of the above problems are solved and applied to the study of dichotomic behavior of dynamical systems.

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