Abstract
A Hilbert space operator is a generalized n-projection, , if . The product AB of a commuting pair A, B of -operators is a -operator. The converse fails. We prove that if and , then implies are if and only if A and B are normal operators. Translated to tensor products (and upon identifying the tensor product with the left-right multiplication operator acting on the Hilbert–Schmidt bimodule ) this says that (resp., ) is a -operator implies are if and only if A and B are normal operators.
Acknowledgments
The current version of the manuscript owes a great debt to a referee for his/her critical comments. It is the authors' pleasure to thank the referee.
Disclosure statement
No potential conflict of interest was reported by the author(s).