Let A be a bounded linear operator on a Banach space X. We investigate the conditions of existing rank-one operator B such that I+f(A)B is invertible for every analytic function f on sigma(A). Also we compare the invariant subspaces of f(A)B and B. This work is motivated by an operator method on the Banach space ell^2 for solving some PDEs which is extended to general operator space under some ...

In this paper, we discuss a class of problems that arises in an m-machine ow-shop operated by a single operator.

Based on the quantization of one-photon electromagnetic field described in terms of the Riemann-Silberstein complex vector F, we construct the eigenvector set of F, this set is orthonormal and complete, with which we introduce the phase operator for one-photon state. It is shown that this phase operator manifestly exhibits phase behaviour.

In this work we prove that the one-body position operator for periodic systems have recently proposed [Phys. Rev. B 99, 205144 (2019)] is unique modulo a phase factor and an additive constant. The proof uses several general physical constraints should satisfy. We show these are sufficient to uniquely define compatible with boundary conditions.