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  • 1 Technische Universität Wien Institut für Analysis, Technische Mathematik und Versicherungsmathematik, E114-1 Wiedner Hauptstrasse 8–10 1040 Wien Austria Wiedner Hauptstrasse 8–10 1040 Wien Austria
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Abstract  

Let ℌ be a Hilbert space and F(ℌ) be the full Fock space generated by ℌ. For v ∈ ℌ, the (left) creation operator l(v) : F(ℌ) → F(ℌ),f↦ v ⊗ f, and its adjoint, the (left) annihilation operator l(v)*, are defined. If v, w ∈ℌ are orthonormal, it is proved that the spectrum of the operator l(v) + l(w)* is purely continuous and conincides with the closed unit disk.

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