Some new results for Hua-type operator matrices.

Let A i ( i = 1 , 2 , … , n ) be strict contractions on a Hilbert space H . The n × n operator matrix H n ( A 1 , A 2 , ⋯ , A n ) = ( ( I − A j ⁎ A i ) − 1 ) i , j = 1 n is called a Hua-type operator matrix. In this note, we mainly investigate some results which are related to the Hua-type operator matrix. We firstly give some equivalent conditions for the positivity of n × n operator matrices ( I − A j ⁎ A i ) i , j = 1 n . Then the equation min { ‖ H 2 ( A 1 , A 2 ) ‖ : ‖ A 1 ‖ < 1 , ‖ A 2 ‖ < 1 } = 2 is shown. In particular, some equivalent conditions for strict contractions A 1 and A 2 such that ‖ H 2 ( A 1 , A 2 ) ‖ = 2 are obtained. [ABSTRACT FROM AUTHOR]