@Article{Stochel2006,
author = "Stochel, Jerzy Bartłomiej",
title = "A remark on generalized commutation relation and subnormality",
journal = "Opuscula Math.",
year = "2006",
volume = "26",
number = "1",
pages = "151--160",
doi = "http://dx.doi.org/10.7494/OpMath.2006.26.1.151",
url = "http://dx.doi.org/10.7494/OpMath.2006.26.1.151",
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",
issn = "1232-9274"
}