CHARACTERIZATION OF SUM OF ORTHOGONAL PROJECTION OPERATORS ON HILBERT SPACE - Humam, Afif
An orthogonal projection is a linear transformation which has two properties, idempotent and selfadjoint. This thesis contains characterization of operators which are expressible as a sum of finitely many orthogonal projections on a Hilbert space. In general, the necessary and suffcient conditions of an operator positive T such that T is expressible as a sum of finitely many of orthogonal projections is for some Hilbert space N, T o0N is unitarily equivalent to an operator matrix which diagonal elements are identity operators. In addition, there also some characterizations of sum of finitely many of orthogonal pro- jections on infinite dimensional separable Hilbert space based on the essential norm. A positive operator whose essential norm is less than one is sum of finitely many orthogonal projections if and only if if it has an integer trace and its trace is greater than or equal to its rank.