Geodesic
A peculiarity of the creation operator
Glasgow mathematical journal, Tome 44 (2002) no. 1, pp. 137-147

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It is shown that the creation operator is the only (up to a multiplicative constant) injective weighted shift all of whose translations (or at least one) are still injective weighted shifts regardless of what the weight sequences and the bases are. A similar result is true for the annihilation operator as well as for the Heisenberg and Schrödinger couples. 
Stochel, Jan; Szafraniec, Franciszek Hugon. A peculiarity of the creation operator. Glasgow mathematical journal, Tome 44 (2002) no. 1, pp. 137-147. doi: 10.1017/S0017089502010091
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