We define the energy functional for a bounded linear operator acting on a Hilbert space through a newly defined non-Euclidean metric on its resolvent set , where the vector . We investigate the extremal values of with respect to the change of . We conduct an in-depth study of the case when is the classical Volterra operator on . Our main theorem suggests a likely connection between the energy functional and the invariant subspace problem.
"Energy functional of the Volterra operator." Banach J. Math. Anal. 13 (2) 255 - 274, April 2019. https://doi.org/10.1215/17358787-2018-0029