Spectrum of Certain Unbounded Composition Transformations in l2

Abstract

Let l² be the Hilbert space of all square summable sequences of complex numbers under the standard inner product on it. Let C_Φ be an unbounded densely defined composition transformation in l² induced by a function Φ on N into itself such that n ∈Φ^-1(n) for each n in the range of Φ. We prove that spectrum of C_Φ is all of C.