Douglas Theorem and its variants


主讲人:Professor M. S. Moslehian,Ferdowsi University of Mashhad




主讲人介绍:Mohammad Sal Moslehian is a (full-time) professor of mathematics at Ferdowsi  University of Mashhad. He received a Master of Science degree in 1991 and a  Doctor of Science degree in 1999.

内容介绍:Douglas Theorem on equivalence of factorization, range inclusion, and  majorization of operators states that if A and B are in the algebra of bounded  linear operators on a Hilbert space H, then the following statements are  equivalent: (i) R(A)⊆R(B); (ii) A = BC for some C∈B(H ); (iii) AA≤ kBBfor some k  ≥ 0. In this talk, we investigate some generalizations, variants, and  consequences of this theorem in various settings including Hilbert C-modules.