Positive semi-definite matrices of adjointable operators on Hilbert C*-modules

By Qingxiang Xu, Lijuan Sheng. 2008

108 citations recorded by the source corpus.

Abstract Let A be a C ∗ -algebra, H , K be two Hilbert A -modules, and B be an adjointable operator from H to K . In this paper, we prove that the Moore–Penrose inverse of B exists if and only if B has closed range. In addition, some known results about the Moore–Penrose inverses acting on Hilbert spaces, as well as in C ∗ -algebras are extended in the context of Hilbert C ∗ -modules. As an application, a characterization of positive semi-definite matrices of adjointable operators with respect to an orthogonal pair of a Hilbert C ∗ -module is given.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bbbd28cdd4c827d0af45f65267415eddf4747489

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Dragan S. Djordjevi'c
2. Chunyuan Deng
3. Dragana S. Cvetkovic-Ilic

In Computational Theory and Mathematics

1. Dragan S. Djordjevi'c
2. Chunyuan Deng
3. Dragana S. Cvetkovic-Ilic

In Mathematical Physics

1. Dragan S. Djordjevi'c
2. Chunyuan Deng
3. Dragana S. Cvetkovic-Ilic

Citations in the corpus

• REVERSE ORDER LAW FOR THE MOORE-PENROSE INVERSE OF CLOSED-RANGE ADJOINTABLE OPERATORS ON HILBERT C*-MODULES (2014, background): “Moreover, T † exists if and only if R(T ) is closed in N (see [14]).”