In this paper, local symmetry of Birkhoff orthogonality is considered in the positive cones of
C⁎-algebras. For the positive cone A+ of a C⁎-algebra A, the notion of A+-local left (or right) …

In this paper, complete characterizations of left (or right) symmetric points for strong Birkhoff
orthogonality in B (H, K) B (H, K) and K (H, K) K (H, K) are given, where H, KH, K are …

We study the relation of mutual strong Birkhoff–James orthogonality in two classical C^* C∗-
algebras: the C^* C∗-algebra B (H) B (H) of all bounded linear operators on a complex …

Complete characterizations of left or right symmetric points for (strong) Birkhoff orthogonality
in von Neumann algebras and abelian unital C⁎-algebras are given. As an application, we …

In the present paper, we study infinite dimensional orthogonality preserving the second-
order nonlinear Markov operators. It is proved that subjectivity of the second-order nonlinear …

Geometric nonlinear classification of Hilbert $$C^*$$ -modules based on strong Birkhoff–James
orthogonality | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A …

We survey mainly recent results on the orthogonality relations in normed linear spaces
related to norm derivatives. We will focus on fundamental properties of norm derivatives …

We introduce and study modular Birkhoff–James orthogonality for typical Banach modules B
(X, Y) B (X, Y) and K (X, Y), K (X, Y), where XX and YY are Banach spaces. We present some …

A new notion of non-linear isomorphisms between Banach modules is introduced based on
modular Birkhoff-James orthogonality. It is shown that a (possibly non-linear) bijective …

Let K(H) be the C^*-algebra of compact op\-erators on a Hilbert space H. Let E be a Hilbert
K(H)-mod\-ule and L(E) the C^*-algebra of all adjointable maps on E. In this paper, we prove …