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A peculiarity of the creation operator

Published online by Cambridge University Press:  18 July 2002

Jan Stochel  and
Franciszek Hugon Szafraniec
Jan Stochel
Affiliation:
Instytut Matematyki, Uniwersytet Jagielloński, ul. Reymonta 4, PL-30059 Kraków, Poland e-mail: stochel@im.uj.edu.pl and fhszafra@im.uj.edu.pl
Franciszek Hugon Szafraniec
Affiliation:
Instytut Matematyki, Uniwersytet Jagielloński, ul. Reymonta 4, PL-30059 Kraków, Poland e-mail: stochel@im.uj.edu.pl and fhszafra@im.uj.edu.pl
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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 44 , Issue 1 , January 2002 , pp. 137 - 147
Copyright
2002 Glasgow Mathematical Journal Trust

Footnotes

Dedicated to the memory of I. E. Segal.
The research resulting in this paper was supported at its final stage by the KBN grant #2 P03A 004 17.