A note on the functional calculus for unbounded self-adjoint operators

作者：Fitzpatrick Patrick M^*

来源：Journal of Fixed Point Theory and Applications, 2013, 13(2): 633-640.

DOI：10.1007/s11784-013-0139-y

• Functional calculus
• Borel function
• self-adjoint operator
• Riesz-Lorch theorem

Two theorems of Riesz and Lorch (1936) are used to pass directly from the functional calculus for bounded symmetric operators to that for unbounded self-adjoint operators, thereby considerably shortening the passage via the spectral resolution for unbounded self-adjoint operators, and making particularly transparent the manner in which properties of the functional calculus for bounded operators are inherited by those which are unbounded.

• 出版日期2013-6