Spectrums of equivalent Schauder operators

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 $σ_e(A)$, then there exists a unitary spread operator $U$ such that the Schauder spectrum $σ_S(UA)$ contains a ring which is depended by the essential spectrum; if there is only one point in $σ_e(A)$ and satisfies some conditions then there exists a unitary spread operator $U$ such that the Schauder spectrum $σ_S(UA)$ contains the circumference which is depended by the essential spectrum.

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