# Spectral properties of block Jacobi matrices

## TL;DR

This paper investigates the spectral characteristics of block Jacobi matrices with operator entries, providing conditions for continuous spectra, asymptotic behaviors of eigenvectors, and criteria for indeterminacy.

## Contribution

It introduces new conditions for the spectrum to be continuous and analyzes eigenvector asymptotics for block Jacobi matrices with operator entries.

## Key findings

- Conditions for continuous spectrum established
- Asymptotic behavior of eigenvectors characterized
- Criteria for spectral indeterminacy provided

## Abstract

We study the spectral properties of bounded and unbounded Jacobi matrices whose entries are bounded operators on a complex Hilbert space. In particular, we formulate conditions assuring that the spectrum of the studied operators is continuous. Uniform asymptotics of generalised eigenvectors and conditions implying complete indeterminacy are also provided.