A peculiarity of the creation operator

Jan Stochel, Franciszek Hugon Szafraniec
2002 Glasgow Mathematical Journal  
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 Schro¨dinger couples.
doi:10.1017/s0017089502010091 fatcat:jhaw5pnebrdglhmoh5gmlvi56q