Commuting unilateral shifts
Author:
James A. Deddens
Journal:
Proc. Amer. Math. Soc. 25 (1970), 96-99
MSC:
Primary 47.10
DOI:
https://doi.org/10.1090/S0002-9939-1970-0265958-3
MathSciNet review:
0265958
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Abstract | References | Similar Articles | Additional Information
Abstract: Examples are given to show that two commuting unilateral shifts (of dimension $\infty ,\infty$ or $m,n$ with $2 \leqq m,\;n < \infty$) need not commute with a unilateral shift of multiplicity one.
- Arlen Brown and P. R. Halmos, Algebraic properties of Toeplitz operators, J. Reine Angew. Math. 213 (1963/64), 89–102. MR 160136, DOI https://doi.org/10.1007/978-1-4613-8208-9_19 J. A. Deddens, Coisometric extensions of semigroups of operators, Thesis, Indiana University, Bloomington, Ind., 1969.
- P. Erdős, H. S. Shapiro, and A. L. Shields, Large and small subspaces of Hilbert space, Michigan Math. J. 12 (1965), 169–178. MR 178349
- Peter A. Fillmore, Notes on operator theory, Van Nostrand Reinhold Mathematical Studies, No. 30, Van Nostrand Reinhold Co., New York-London-Melbourne, 1970. MR 0257765
- Paul R. Halmos, Shifts on Hilbert spaces, J. Reine Angew. Math. 208 (1961), 102–112. MR 152896, DOI https://doi.org/10.1515/crll.1961.208.102
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Additional Information
Keywords:
Inner functions,
Blaschke products,
backward translation,
isometry
Article copyright:
© Copyright 1970
American Mathematical Society