Fuglede-Putnam type commutativity theorems for operators
arXiv:2101.06725
Abstract
Fuglede-Putnam theorem is not true in general for operators on Hilbert spaces. We prove that under some conditions the theorem holds good. If the adjoint operation is replaced by Moore-Penrose inverse in the theorem, we get Fuglede-Putnam type theorem for operators -- however proofs are totally different. Finally, interesting results on operators have been proved using several versions of Fuglede-Putnam type theorems for operators on Hilbert spaces.
10 pages