Study on Birkhoff orthogonality and symmetry of matrix operators

Abstract We focus on the problem of generalized orthogonality matrix operators in operator spaces. Especially, ℬ ( l 1 n , p ) ≤ ∞ {\mathcal{ {\mathcal B} }}\left({l}_{1}^{n},{l}_{p}^{n})\left(1\le p\le \infty ) , we characterize Birkhoff orthogonal elements a certain class and point out conditions for which satisfy Bhatia-Šemrl property. Furthermore, give some conclusions are related to In space, such as }}\left({l}_{\infty }^{n}) properties left right symmetry discussed. Moreover, equivalence condition < }}\left({l}_{p}^{n})\left(1\lt p\lt is obtained.