Abstract

Let S be the unilateral shift on the basis { e n:n ∈ N }. It will be proven that S is similar to S+ Lif∑ iJ∈N|( Lej, ei)|<1. Analogous results about the bilateral shift and weighted shifts are proved by the same algorithm. In the process, the operator Δ: X↦ AX − XB and its one-sided inverses are also studied.

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