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- Title
On the parallel sum of positive operators, forms, and functionals.
- Authors
Tarcsay, Zs.
- Abstract
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 for fixed $${x \in H}$$ . The purpose of this paper is to provide a factorization of the parallel sum of the form $${J_A PJ_A^*}$$ where $${J_A}$$ 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 $${\bar{E}^{\prime}}$$ , and of representable positive functionals on a $${^*}$$ -algebra.
- Subjects
OPERATOR theory; FUNCTIONALS; HILBERT space; FACTORIZATION; ORTHOGRAPHIC projection
- Publication
Acta Mathematica Hungarica, 2015, Vol 147, Issue 2, p408
- ISSN
0236-5294
- Publication type
Academic Journal
- DOI
10.1007/s10474-015-0533-6