Abstract
Let be a semi-finite von Neumann algebra,
be the set of all τ-measurable operators,
be the generalized singular number of
and
be a concave function. We proved that if
are normal operators in
, then
is submajorized by
. As an application, we obtained that if x is a matrix of normal operators
in
, then
is submajorized by
.
Acknowledgments
We thank the referee for very useful comments, which improved the paper. R. Ahat was partially supported by NSFC grant No. 11771372, and M. Raikhan was partially supported by project AP05131557 of the Science Committee of Ministry of Education and Science of the Republic of Kazakhstan.
Disclosure statement
No potential conflict of interest was reported by the author(s).