The invertibility of 2X2 operator matrices
Junjie Huang, Junfeng Sun, Alatancang Chen, Carsten Trunk
TL;DR
This paper investigates the conditions under which 2x2 operator matrices are invertible, focusing on right invertible row operators and applying the findings to Hamiltonian operator matrices.
Contribution
It provides a new characterization of invertibility for 2x2 operator matrices using space decomposition techniques, with applications to Hamiltonian matrices.
Findings
Characterization of invertibility via space decomposition
Criteria for invertibility of Hamiltonian operator matrices
Analysis of right invertible row operators
Abstract
In this paper the properties of right invertible row operators, i.e., of 1X2 surjective operator matrices are studied. This investigation is based on a specific space decomposition. Using this decomposition, we characterize the invertibility of a 2X2 operator matrix. As an application, the invertibility of Hamiltonian operator matrices is investigated.
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Taxonomy
TopicsMatrix Theory and Algorithms · Holomorphic and Operator Theory · Advanced Topics in Algebra