  Assume that $T_1,T_2$ are equivalent Schauder operators. In this paper, we
show that even in this case their Schauder spectrum may be very different in
the view of operator theory. In fact, we get that if a self-adjoint Schauder
operator $A$ has more than one points in its essential spectrum $\sigma_e(A)$,
then there exists a unitary spread operator $U$ such that the Schauder spectrum
$\sigma_S(UA)$ contains a ring which is depended by the essential spectrum; if
there is only one point in $\sigma_e(A)$ and satisfies some conditions then
there exists a unitary spread operator $U$ such that the Schauder spectrum
$\sigma_S(UA)$ contains the circumference which is depended by the essential
spectrum.

Functional Analysis