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Spectral representations of unbounded non-linear operators on Hilbert space
Journal article   Open access   Peer reviewed

Spectral representations of unbounded non-linear operators on Hilbert space

Pacific journal of mathematics, Vol.111(1), pp.93-104
1984
DOI: 10.2140/pjm.1984.111.93
url
https://doi.org/10.2140/pjm.1984.111.93View
Published (Version of record) Open Access

Abstract

Let H be a separable complex ∞-dimensional Hubert space and let F be the Fock space of symmetric tensors over H. We consider non-linear operators T from H to F defined on a dense subspace D in H with range in W. A symmetry and reality condition is imposed on the operators T under consideration. They are generally unbounded and have different extensions T defined on subspaces D in H containing D. Generalizing a result of Arveson for bounded operators (alias functions from H to F), we show that if T is affiliated with a maximal abelian von Neumann algebra in B(H), then it follows that there is an extension T of T which is unitarily equivalent to a (non-linear) multiplication operator. © 1984 by Pacific Journal of Mathematics.
Physics Exact sciences and technology Function theory, analysis General Mathematical methods in physics

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