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On Shift Operators

Published online by Cambridge University Press:  20 November 2018

J. R. Holub
J. R. Holub*
Affiliation:
Department of Mathematics, Virginia Polytechnic Institute and State University BLacksburg, Virginia24061
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Abstract

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A definition of an isometric shift operator on a Banach space is given which extends the usual definition of a shift operator on a separable Hilbert space. It is shown that there is no such shift on many of the common Banach spaces of continuous functions. The associated ideas of a semi-shift and a backward shift are also introduced and studied in the case of continuous function spaces.

Keywords

47B3847A65
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 1 , 01 March 1988 , pp. 85 - 94
Copyright
Copyright © Canadian Mathematical Society 1988

References

1. Crownover, R. M., Commutants of shifts on Banach spaces, Michigan Math. J. 19 (1972), pp. 233–247.Google Scholar
2. Dunford, N. and Schwartz, J., Linear Operators, Part I, Interscience Publishers, New York, 1963.Google Scholar
3. Geller, R., Cyclic vectors and parts of the spectrum of a weighted shift, Trans. Amer. Math. Soc. 146(1969), pp. 69–85.Google Scholar
4. Geller, R., Operators commuting with a weighted shift, Proc. Amer. Math. Soc. 23 (1969), pp. 538–545.Google Scholar
5. Grabiner, S., Weighted shifts and Banach algebras of power series, Amer. J. Math. 97 (1975), pp. 16–42.Google Scholar
6. Grabiner, S., Unicellular shifts on Banach spaces, Journal of Operator Theory 8 (1982), pp. 157–165.Google Scholar
7. Rudin, W., Real and complex analysis, 2nd Ed., McGraw-Hill, Inc., 1966.Google Scholar
8. Singer, I., Bases in Banach spaces I, Springer-Verlag, Berlin, 1970.Google Scholar