1. CMB 2011 (vol 54 pp. 456)
|On Operator Sum and Product Adjoints and Closures|
We comment on domain conditions that regulate when the adjoint of the sum or product of two unbounded operators is the sum or product of their adjoints, and related closure issues. The quantum mechanical problem PHP essentially selfadjoint for unbounded Hamiltonians is addressed, with new results.
Keywords:unbounded operators, adjoints of sums and products, quantum mechanics
2. CMB 2011 (vol 54 pp. 498)
|On the Adjoint and the Closure of the Sum of Two Unbounded Operators|
We prove, under some conditions on the domains, that the adjoint of the sum of two unbounded operators is the sum of their adjoints in both Hilbert and Banach space settings. A similar result about the closure of operators is also proved. Some interesting consequences and examples "spice up" the paper.
Keywords:unbounded operators, sum and products of operators, Hilbert and Banach adjoints, self-adjoint operators, closed operators, closure of operators