Bilateral Shorted Operators and Parallel Sums

By Jorge Antezana, Gustavo Corach, Demetrio Stojanoff. 2005

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In this paper we study shorted operators relative to two different subspaces, for bounded operators on infinite dimensional Hilbert spaces. We define two notions of “complementability” in the sense of Ando for operators, and study the properties of the shorted operators when they can be defined. We use these facts in order to define and study the notions of parallel sum and substraction, in this Hilbertian context.

Subfields: Algebra and Number Theory, Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/1916ea5ac60e3263ae873fe76bc6ab931adc629f