Preserving some orthogonal operators on Banach spaces
Dhuha Najah Hossein Al-Khalidi · Al-Qadisiyah Journal Of Pure Science · 2024
In this article, the Birkhoff–James orthogonality on a real Banach space X from linear operators and the category of conjugate linear mapping Φ:B(H) →B(H) that keep the strong orthogonality in both spaces is explored. We also investigate left orthogonal Birkhoff-James symmetry of linear operators defined on X. We also prove, for every strictly convex and smooth real Banach space X, is left symmetric if and only if operators are zero. We also examine operator spaces and determine its left symmetric operators.