Question

inverse of a positive operator with spectral radius less than 1

Answer 1

Answer:

Let A be a positive matrix, assume that its spectral radius ρ(A) = 1 (otherwise consider A/ρ(A)). Hence, there exists an eigenvalue λ on the unit circle, and all the other eigenvalues are less or equal 1 in absolute value. ... Moreover, if Ax = λx then Amx = λmx thus λm − ε is an eigenvalue of T.