Affiliation:
1. School of Mathematics and Computer Sciences, Damghan University, Damghan, Iran
Abstract
We show that if X and Y are two non-zero Hilbert-Schmidt operators, then for
any ? ? 0, cos2 ?X,Y ? 1/1 + ? ?cos?|X*|,|Y*| ? cos?|X|,|Y| |?X,Y?|/?X?2
?Y?2 + ?/1 + ? cos?|X*|,|Y*| cos?|X|,|Y| ? cos?|X*|,|Y*| cos?|X|,|Y| .
Here ?A,B denotes the angle between non-zero Hilbert-Schmidt operators A and
B. This enables us to present some inequalities for the Hilbert-Schmidt
norm. In particular, we prove that ?X+Y?2 ? ?? 2+1/2 ?|X|+|Y|?2.
Publisher
National Library of Serbia