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.