We offer a new definition of $varepsilon$-orthogonality in normed spaces, and we try to explain some properties of which. Also we introduce some types of $varepsilon$-orthogonality in an arbitrary  $C^ast$-algebra $mathcal{A}$, as a Hilbert $C^ast$-module over itself, and investigate some of its properties in such spaces. We state some results relating range-kernel orthogonality in $C^*$-algebras.

In this paper, the notion of rank-k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated. Moreover, for ϵ > 0; the notion of Birkhoff-James approximate orthogonality sets for ϵ-higher rank numerical ranges of rectangular matrix polynomials is also introduced and studied. The proposed denitions yield a natural genera...

We study the norm derivatives in context of Birkhoff–James orthogonality real Banach spaces. As an application this, we obtain a complete characterization left-symmetric points and right-symmetric space terms derivatives. strong $$\ell _1^n$$ _\infty ^n$$ also relation defined by some newly introduced variation orthogonality. further orthogonality, approximate smoothness attainment bounded bili...

We show that the approximate quasi-orthogonality of two operator algebras is equivalent to being approximately private relative their conditional expectation quantum channels. Our analysis based on a characterization measure orthogonality in terms Choi matrices and Kraus operators for completely positive maps. present examples drawn from different areas information.

Two different notions of approximate Birkhoff–James orthogonality in normed linear spaces have been introduced by Dragomir and Chmieliński. In the present paper we consider a global local symmetry related to each two definitions. We prove that considered is approximately symmetric sense all finite-dimensional Banach spaces. For other case, for polyhedral spaces, equivalent some newly geometric ...