Range additivity, shorted operator and the Sherman-Morrison-Woodbury formula

2014/09/05 by M. Laura Arias, Arias, M. Laura, Gustavo Corach +3
Mathematics · #46C07- 47A64 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46C07- #msc:47A64

paper · pdf · doi:10.48550/arxiv.1409.1958

arxiv created 2014/09/05 · arxiv updated 2014/09/09

Abstract

We say that two operators A, B have the range additivity property if R(A + B) = R(A) + R(B). In this article we study the relationship between range additivity, shorted operator and certain Hilbert space decomposition known as compatibility. As an application, we extend to infinite dimensional Hilbert space operators a formula by Fill and Fishkind related to the well-known Sherman-Morrison-Woodbury formula.

Related

• Operator factorization of range space relations
• Operators with compatible ranges
• An indefinite range inclusion theorem for triplets of bounded linear operators on a Hilbert space
• Projections in operator ranges
• Operator Ranges and Spaceability: Extending a Result of Kitson and Timoney