Numerical range of weighted composition operators on the quaternionic Fock space

Abstract

  In this paper, we use unitary equivalence to transform a general normal weighted compostion operator into a new weighted composition operator with constant multiplier. And then the spherical spectrum is used to characterize the convex hull of numerical range of two types normal bounded weighted composition operators on quaternionic Fock space F2(H). Especially we explicitly formulate their numerical radiiand present several nontrivial examples.