Partial isometries, contractions and EP matrices

Abstract

Some new results are derived for complex n × n contractions and partial isometries, illustrating the natural way in which the EP concept enters the study of these matrices. It is shown that for any contraction K, 1 − K is EP and R(I − KK*)⊆R(I − K). where R(⋅) denotes the range of (⋅). It is further proven that if are n × n contractions with K 1 and L 1 of size k × k, then are also EP.