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Abstract and Applied Analysis
Volume 2006 (2006), Article ID 78928, 13 pages

Bourgin-Yang-type theorem for a-compact perturbations of closed operators. Part I. The case of index theories with dimension property

1Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, México DF 04510, Mexico
2Department of Mathematics and Computer Science, Netanya Academic College, Netanya 42365, Israel
3Faculty of Mathematics, Voronezh State University, 1 Universitetskaya Pl., Voronezh 394006, Russia

Received 26 June 2005; Accepted 1 July 2005

Copyright © 2006 Sergey A. Antonyan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A variant of the Bourgin-Yang theorem for a-compact perturbations of a closed linear operator (in general, unbounded and having an infinite-dimensional kernel) is proved. An application to integrodifferential equations is discussed.