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      Embeddings, operator ranges, and Dirac operators

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      Author(s)
      Cojuhari, P.
      Gheondea, A.
      Date
      2011
      Source Title
      Complex Analysis and Operator Theory
      Print ISSN
      1661-8254
      Electronic ISSN
      1661-8262
      Publisher
      Springer Basel
      Volume
      5
      Issue
      2
      Pages
      941 - 953
      Language
      English
      Type
      Article
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      Abstract
      Motivated by energy space representation of Dirac operators, in the sense of K. Friedrichs, we recently introduced the notion of closely embedded Kreǐn spaces. These spaces are associated to unbounded selfadjoint operators that play the role of kernel operators, in the sense of L. Schwartz, and they are special representations of induced Kreǐn spaces. In this article we present a canonical representation of closely embedded Kreǐn spaces in terms of a generalization of the notion of operator range and obtain a characterization of uniqueness. When applied to Dirac operators, the results differ according to a mass or a massless particle in a dramatic way: in the case of a particle with a nontrivial mass we obtain a dual of a Sobolev type space and we have uniqueness, while in the case of a massless particle we obtain a dual of a homogenous Sobolev type space and we lose uniqueness. © 2010 Elsevier Inc.
      Keywords
      Closed embedding
      Dirac operator
      Homogenous Sobolev space
      Kernel operator
      Krein space
      Operator range
      Permalink
      http://hdl.handle.net/11693/12069
      Published Version (Please cite this version)
      http://dx.doi.org/10.1007/s11785-010-0066-5
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      • Department of Mathematics 653
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