Abstract: Unbounded block operator matrix widely appears in the fields of system theory, nonlinear analysis and evolution equation problems, and has been widely concerned in both theory and practical application. Firstly, the decomposability of unbounded block operator matrix is characterized by using local spectrum theory. Secondly, the condition that the decomposability of operator matrix remains diagonally stable is given, and some local spectral properties of block operator matrix are generalized and obtained. Finally, as an application, the decomposability of Hamilton operator is investigated and illustrated with examples.

Key words: decomposability, unbounded block operator matrix, local spectral property, Hamiltonian operator