Classes of Idempotents in Hilbert Space

Abstract

An idempotent operator E in a Hilbert space H(E2= 1) is written as a 2 × 2 matrix in terms of the orthogonal decomposition H=R(E)⊕R(E)⊥(R(E) is the range of E) as (Formula Presented). We study the sets of idempotents that one obtains when E1 , 2: R(E)⊥→ R(E) is a special type of operator: compact, Fredholm and injective with dense range, among others.