Abstract: The author considered the pseudoanti self adjoint property of compact normal operators in quaternion Hilbert spaces. The author used slice functional calculus of operators and the theory of spherical spectrum to characterize the spherical spectrum of compact normal pseudoanti self adjoint operators, and gave the relation between the self adjoint property and pseudoanti self adjoint property of the operators.

Key words: quaternion； compact normal； pseudoanti self adjoint , operator； spherical spectrum