Extensions of symmetric infinite Jacobi operator

Abstract

A space of positive boundary values is constructed for a positive definite minimal symmetric operator generated by an infinite Jacobi matrix in limit-circle case. A description of all solvable, maximal dissipative (accumulative) solvable, self-adjoint solvable, positive definite self-adjoint and non-positive definite self-adjoint extensions of such a symmetric operator is given in terms of boundary conditions at infinity.

Keywords:

• infinite Jacobi matrix
• symmetric operator
• space of positive boundary values
• solvable extensions
• positive definite self-adjoint and non-self-adjoint extensions
• maximal dissipative operator

AMS Subject Classifications:

• Primary 47B36
• 47B25
• 47A20
• 47B39
• 47B44 Secondary 39A10
• 39A70
• 39A12