I am interested in obtaining the following paper:
G. K. Kalisch, "On operators with large point spectrum," Scripta Math. 29 No. 3-4, (1973), 371-378.
According to Ben Mathes, "Strictly Cyclic Algebras with Arbitrary Prescribed Gelfand Spectrum" (2008), it contains the following result. Let $X=L_2([0,1]\times[0,1])$ and let $A\subset\mathbb{C}$ be any compact set. Then there exists an operator $T\in\mathcal{L}(Y)$ satisfying $\sigma(T)=\sigma_p(T)=A$, i.e. where both the spectrum and the point spectrum of $T$ are equal to $A$, and $Y$ is a closed subspace of $X$.
Actually, what I really need to do is find/construct an operator $T$ on a separable Banach space $X$ satisfying $\sigma(T)=\sigma_p(T)=$ the unit circle. Kalisch's operator will do it, but then I'd need to verify that it really is what Mathes says it is. But it doesn't have to be Kalisch's operator. As long as $X$ is separable and $\sigma(T)=\sigma_p(T)=$ the unit circle, that is enough.
Thanks!
