Abstract We focus on the problem of generalized orthogonality matrix operators in operator spaces. Especially, ℬ ( l 1 n , p ) ≤ <m:m...

A generalized N-point Birkhoff–Young quadrature of interpolatory type, with the Chebyshev weight, for numerical integration of analytic functions is considered. The nodes of such a quadrature are characterized by an orthogonality relation. Some special cases of this quadrature formula are derived. 2011 Elsevier Inc. All rights reserved.

In this short paper we answer a question posed by Chmieliński in [Adv. Oper. Theory 1 (2016), no. 1, 8–14]. Namely, we prove that among normed spaces of dimension greater than two, only inner product spaces admit nonzero linear operators which reverse the Birkhoff orthogonality.

We study best approximations to compact operators between Banach spaces and Hilbert spaces, from the point of view Birkhoff-James orthogonality semi-inner-products. As an application present study, some distance formulae are presented in space operators. The special case bounded linear functionals as is treated separately applications reflexive, strictly convex smooth discussed. An explicit exa...

Associated to Birkhoff orthogonality, we study angles in a normed space and present some of their basic properties. We also discuss how decide whether an angle is more acute or obtuse than another. In addition, given two vectors $x$ $y$ space, the formula for `cosine' from which can, principal, compute angle. Some examples will be presented.

A kind of generalized quadrature formulae of maximal degree of precision for numerical integration of analytic functions is considered. Precisely, a general weighted quadrature of Birkhoff-Young type with 4n+3 nodes and degree of precision 6n+5 is studied. Its nodes are characterized by an orthogonality relation and a general numerical method for their computation is given. Special cases and nu...

We try to control many cardinal characteristics by working with a notion of orthogonality between two families of forcings. We show that b < g is consistent. This work is dedicated to James Baumgartner on the occasion of his 60th birthday.

We prove the orthogonality (in the sense of Birkhoff) of the range and the kernel of an important class of elementary operators with respect to the Schatten p-class. 1. Introduction. Let H be a separable infinite-dimensional complex Hilbert space and let B(H) denote the algebra of all bounded operators on H into itself. Given A, B ∈ B(H), we define the generalized derivation δ A,B : B(H) B(H) b...

We are interested in the investigation of the orthogonality (in the sense of Birkhoff) of the range of an elementary operator and its kernel. 1. Introduction. Let H be a separable infinite-dimensional complex Hilbert space and let B(H) denote the algebra of all bounded operators on H into itself. Given A, B ∈ B(H), we define the generalized derivation δ A,B : B(H) B(H) by δ A,B (X) = AX −XB and...