Journal article
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
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.
Details
- Title: Subtitle
- Spectral representations of unbounded non-linear operators on Hilbert space
- Creators
- P. E. T Jorgensen - Univ. Pennsylvania, dep. math
- Resource Type
- Journal article
- Publication Details
- Pacific journal of mathematics, Vol.111(1), pp.93-104
- DOI
- 10.2140/pjm.1984.111.93
- ISSN
- 0030-8730
- eISSN
- 1945-5844
- Publisher
- University of California, Department of Mathematics
- Language
- English
- Date published
- 1984
- Academic Unit
- Mathematics
- Record Identifier
- 9984240871302771
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