Norm-parallelism in the geometry of Hilbert [formula omitted]-modules

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, elements of a Hilbert C∗-module over the C∗-algebra of compact operators and elements of an arbitrary C∗-algebra. We also consider the characterization of norm parallelism problem for operators on a finite dimensional Hilbert space when the operator norm is replaced by the Schatten p-norm. Some applications and generalizations are discussed for certain elements of a Hilbert C∗-module.