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A remark on generalized commutation relation and subnormality

Stochel J.B.

Opuscula Mathematica

2006

Vol. 26, no. 1

151-160

Tillmann [11] 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* = E², 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.