New norm equalities and inequalities for certain operator matrices

Abstract

We prove new norm equalities and inequalities for general n × n tridiagonal and antitridiagonal operator matrices, including pinching type inequalities for weakly unitarily invariant norms.

On $${\mathbb {A}}$$-numerical radius equalities and inequalities for certain operator matrices

“…In Sect. 4 , we extend some recent results of Bani-Domi et al [ 5 ] to the semi-Hilbert space operators. In particular, we obtain certain -numerical radius equalities and pinching type inequalities for tridiagonal and anti-tridiagonal operator matrices.…”

“…By setting in Theorem 4.3 , 4.4 , and 4.5 , we get usual numerical radius equalities proved by Bani-Domi et al [ 5 ] very recently.…”

“…In this section, inspired by the work of Bani-Domi et al [ 5 ], we extend some recent results of [ 5 ] to semi-Hilbert space. Using a similar analysis as used in the previous section, one can employ certain -numerical radius equalities for tridiagonal and anti-tridiagonal operator matrices.…”

“… If in Theorem 4.1 , we have In particular, [see Lemma 1.1 ]. see [ 5 ]. In particular, see [ 21 , Lemma 2.1].…”

“…So, the -numerical radius inequalities in Theorems 4.7 and 4.8 are sharp. For the usual numerical radius, the usual operator norm and the Schatten p -norms, one can visit [ 5 ].…”