Shorting, parallel addition and form sums of nonnegative selfadjoint\n linear relations

2019/12/02 by Yu. M. Arlinskiĭ, Arlinskii, Yu. M.
Computer Science · Mathematics · #47A06 #47A20 #47A64 #Algebraic and Geometric Analysis #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.1912.00910

openalex publication_date 2019/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the operations of shorting and parallel addition from the cone of\nbounded nonnegative selfadjoint operators in a Hilbert space to the set of all\nnonnegative selfadjoint linear relations. New properties of these operations\nand connections with the Cayley transforms are established. It is shown that\nfor a pair of nonnegative selfadjoint linear relations there exist, in general,\ntwo arithmetic--harmonic means. Applications of the arithmetic, harmonic, and\narithmetic--harmonic means to the theory of nonnegative selfadjoint extensions\nof nonnegative symmetric linear relations are given.\n

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