TY  - JOUR
ID  - Stochel2006
LB  - Stochel2006
AU  - Stochel, Jerzy Bartłomiej
TI  - A remark on generalized commutation relation and subnormality
ST  - A remark on generalized commutation relation and subnormality
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2006
VL  - 26
IS  - 1
SP  - 151
EP  - 160
DO  - http://dx.doi.org/10.7494/OpMath.2006.26.1.151
UR  - http://dx.doi.org/10.7494/OpMath.2006.26.1.151
AB  - 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.
KW  - Hilbert space
KW  - generalized commutation relation
KW  - creation operator
KW  - analytic vectors
SN  - 1232-9274
ER  -