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Quasicyclic Subnormal Semigroups

Published online by Cambridge University Press:  20 November 2018

Richard Frankfurt*
Affiliation:
University of Kentucky, Lexington, Kentucky
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Let T(s), s ≧ 0, be a strongly continuous semigroup of bounded operators on a separable Hilbert space . T(s) is said to be quasicyclic if there is a continuum of vectors such that T(s)xt = xs+t for all s, t > 0 and

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Bram, J., Subnormal operators, Duke Math. J. 22 (1955), 7594.Google Scholar
2. Duren, P. L., Theory of H? spaces (Academic Press, N.Y., 1970).Google Scholar
3. Embry, M. R. and Lambert, A., Weighted translation semigroups, Rocky Mtn. J. Math. (to appear).Google Scholar
4. Embry, M. R. and Lambert, A. Subnormal weighted translation semigroups, J. Funct. Anal. 24 (1977), 268275.Google Scholar
5. Frankfurt, R. E., Subnormal weighted shifts and related function spaces, J. Math. Anal. Appl. 52 (1975), 471489.Google Scholar
6. Frankfurt, R. E. Subnormal weighted shifts and related function spaces II, J. Math. Anal. Appl. 55 (1976), 217.Google Scholar
7. Halmos, P. R., Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76 (1970), 887933.Google Scholar
8. Hille, E. and Phillips, R. S., Functional analysis and semigroups (American Mathematical Society Coll. Pub. vol. XXXI, Providence, R.I., 1957).Google Scholar
9. Hoffman, K., Banach spaces of analytic functions (Prentice-Hall, Englewood Cliffs, N.J., 1962).Google Scholar
10. Ito, T., On the commutative family of subnormal operators, J. Fac. Sci. Hokkaido Univ. 14 (1958), 115.Google Scholar
11. Sz-Nagy, B., Spektraldarstellung Linearer Transformationen des Hilbertschen Raumes, Ergebnisse der Mathematik und Ihrer Grenzgebiete, Band 39 (Springer-Verlag, Berlin- Heidelberg-N.Y., 1967).Google Scholar
12. Watson, G. N., A treatise on the theory of Bessel functions (Cambridge Univ. Press, 1966).Google Scholar