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

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. Copyright (c) 2006 Sergey A. Antonyan et al