Opuscula Math. 26, no. 1 (2006), 151-160

 
Opuscula Mathematica

A remark on generalized commutation relation and subnormality

Jerzy Bartłomiej Stochel

Abstract. Tillmann [Tillmann H. G., Zur Eindeutigkeit der Losungen der quanten mechanischen vertauschungrelationen, Acta Sci. Math. (Szeged) 24 (1963), 258-270] proved that every operator \(A\) which fulfils the canonical commutation relation \(A^{*}A - AA^{*} = Id\) is an orthogonal sum of canonical creation operators. We extend this result for operators which fulfil generalized commutation relation \[A^{*}A - AA^{*}= E^2,\text{ where }EA = AE.\] In addition, some inequalities which are helpful in describing analytic vectors of operators \(A^{*}A\), where \(A\) fulfils the generalized commutation relation, are established.

Keywords: Hilbert space, generalized commutation relation, creation operator, analytic vectors.

Mathematics Subject Classification: 47B20, 47B37, 47B47.

Full text (pdf)

Opuscula Mathematica - cover

Cite this article as:
Jerzy Bartłomiej Stochel, A remark on generalized commutation relation and subnormality, Opuscula Math. 26, no. 1 (2006), 151-160

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.