2015/01/08 by Zsigmond Tarcsay, Tarcsay, Zsigmond · 1 citation
Mathematics · #46K10 #47B65 #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Inequalities and Applications #Primary 47B25 #Secondary 28A12 #math.FA #msc:28A12 #msc:46K10 #msc:47B25 #msc:47B65
paper · pdf · doi:10.48550/arxiv.1501.01922
14 pages
arxiv created 2015/01/08 · openalex publication_date 2015/01/08 · arxiv updated 2015/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The parallel sum A:B of two bounded positive linear operators A,B on a Hilbert space H is defined to be the positive operator having the quadratic form inf\(A(x-y) | x-y)+(By | y) | y∈ H\ for fixed x∈ H. The purpose of this paper is to provide a factorization of the parallel sum of the form JAPJA^* where JA is the embedding operator of an auxiliary Hilbert space associated with A and B, and P is an orthogonal projection onto a certain linear subspace of that Hilbert space. We give similar factorizations of the parallel sum of nonnegative Hermitian forms, positive operators of a complex Banach space E into its topological anti-dual E', and of representable positive functionals on a ^*-algebra.