ON THE CONTINUITY OF PROJECTIONS AND A GENERALIZED GRAM-SCHMIDT PROCESS

Abstract

Let ? be an open connected subset of the complex plane C and let T be a bounded linear operator on a Hilbert space H. For ? in ? let e the orthogonal projection onto the null-space of T-?I . We discuss the necessary and sufficient conditions for the map ?? to b e continuous on ?. A generalized Gram- Schmidt process is also given.