Decomposition of a scalar operator into a product of unitary operators with two points in spectrum

Abstract: We consider products of unitary operators with at most two points in their spectra, 1 and . We prove that the scalar operator is a product of k such operators if for . Also we prove that for , only a countable number of scalar operators can be decomposed in a product of four operators from the mentioned class. As a corollary we show that every unitary operator on an infinite-dimensional space is a product of finitely many such operators. [Copyright &y& Elsevier]