C-spectral operators

Abstract

The importance of the spectral theory of operators in Functional Analysis cannot be over emphasized. Spectral theory is in its best form when one considers normal operators in Hilbert spaces. However, for te dimensional spaces one has the reduction to Jordan's Canonical form. In an attempt to generalize this reduction for arbitrary Banach spaces, Dunford introduced the concept of spectral operators. Considerable work has been done in recent times in the study of spectral theory in Banach spaces, almost all of which stems from the pioneering work of Dunford.