Perron-frobenius-type theorems for tridiagonal operators

Abstract

It is proved that in a large class of bounded tridiagonal operators (infinite Jacobi matrices), not necessarily positive or non-negative, positive eigenvalues exist and the eigenvector which corresponds to the greatest of them can be taken strictly positive. It is the unique positive eigenvector up to a constant multiple.

Keywords:

• Perron-Frobenious-type theorems
• tridiagonal operators

AMS:

• 47B05