Spectral resolutions for non-self-adjoint block convolution operators

Abstract

The paper concerns the spectral theory for a class of non-self-adjoint block convolution operators. We mainly discuss the spectral representations of such operators. It is considered the general case of operators defined on Banach spaces. The main results are applied to periodic Jacobi matrices.

Keywords

• spectral operators
• chains
• triangular decomposition
• laurent operators
• jacobi matrices