In the last few decades, the concept of Birkhoff–James orthogonality has been used in
several applications. In this survey article, the results known on the necessary and sufficient …

The Birkhoff–James orthogonality is a generalization of Hilbert space orthogonality to
Banach spaces. We investigate this notion of orthogonality when the Banach space has …

Let B (H) be the C⁎-algebra of all bounded linear operators on a Hilbert space H. Let N (⋅)
be an arbitrary norm on B (H) and I stand for the identity operator. For T∈ B (H), we …

In a normed space we consider an approximate orthogonality relation related to the Birkhoff
orthogonality. We give some properties of this relation as well as applications. In particular …

In this paper we introduce a strong version of the Birkhoff--James orthogonality in Hilbert $
C^* $-modules. More precisely, we consider elements $ x $ and $ y $ of a Hilbert $ C …

In the following we generalize the concept of Birkhoff–James orthogonality of operators on a
Hilbert space when a semi-inner product is considered. More precisely, for linear operators …

Abstract Utilizing the Birkhoff–James orthogonality, we present some characterizations of the
norm-parallelism for elements of B (ℋ) defined on a finite dimensional Hilbert space …

Extending the notion of parallelism we introduce the concept of approximate parallelism in
normed spaces and then substantially restrict ourselves to the setting of Hilbert space …

BIRKHOFF ORTHOGONALITY IN CLASSICAL M-IDEALS Page 1 J. Aust. Math. Soc. 103 (2017),
279–288 doi:10.1017/S1446788716000537 BIRKHOFF ORTHOGONALITY IN CLASSICAL …

Let (X,⟨⋅,⋅⟩) be a Hilbert C∗-module over a C∗-algebra A and let S (A) be the set of states
on A. In this paper, we first compute the norm derivative for nonzero elements x and y of X as …