DECOMPOSABILITY OF NONNEGATIVE r-POTENT OPERATORS ON L^2(X)

R.S. Thukral, A. Marwaha
2015 International Journal of Pure and Applied Mathematics  
We investigate the decomposability of nonnegative compact rpotent operators on a separable Hilbert space L 2 (X ). We provide a constructive algorithm to prove that basis functions of range spaces of nonnegative r-potent operators can be chosen to be all nonnegative and mutually orthogonal. We use this orthogonality to establish that nonnegative compact r-potent operators with range spaces of dimension strictly greater than r − 1 are decomposable.
doi:10.12732/ijpam.v100i1.4 fatcat:kzpwcibwlfelznmjzizpm2lqeu