English

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

Functional Analysis 2014-09-09 v1

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.

Keywords

Cite

@article{arxiv.1409.1958,
  title  = {Range additivity, shorted operator and the Sherman-Morrison-Woodbury formula},
  author = {M. Laura Arias and Gustavo Corach and Alejandra Maestripieri},
  journal= {arXiv preprint arXiv:1409.1958},
  year   = {2014}
}