AVERAGINGS AND QUADRATIC EQUATIONS IN OPERATORS

摘要

In this paper, bounded linear operators in Hilbert space satisfying general quadratic equations are characterized. Necessary and sufficient conditions for sets of operators satisfying two such equations to compare relative to a Weak ordering, are presented. In addition-the averaging operators in finite dimensional spaces are determined and, in this case. it is shown that the averagings are unitary models for all projections. By a counterexample, it is pointed out that the latter result does not in general extend to the infinite dimensional case.