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- W4300681578 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 begin{equation*} inf{(A(x-y),|,x-y)+(By,|,y),|,yin H} end{equation*} for fixed $xin H$. The purpose of this paper is to provide a factorization of the parallel sum of the form $J_APJ_A^*$ 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 $bar{E}'$, and of representable positive functionals on a $^*$-algebra." @default.
- W4300681578 created "2022-10-04" @default.
- W4300681578 creator A5074124208 @default.
- W4300681578 date "2015-01-08" @default.
- W4300681578 modified "2023-10-14" @default.
- W4300681578 title "On the parallel sum of positive operators, forms, and functionals" @default.
- W4300681578 doi "https://doi.org/10.48550/arxiv.1501.01922" @default.
- W4300681578 hasPublicationYear "2015" @default.
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