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UNBOUNDED HERMITIAN OPERATORS ON KOLASKI SPACES

Published online by Cambridge University Press:  30 August 2013

JAMES JAMISON  and
RAENA KING
JAMES JAMISON
Affiliation:
Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, USA e-mail: [email protected]; [email protected]
RAENA KING
Affiliation:
Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, USA e-mail: [email protected]; [email protected]
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Abstract

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We investigate strongly continuous one-parameter (C0) groups of isometries acting on certain spaces of analytical functions which were introduced by Kolaski (C. J. Kolaski, Isometries of some smooth normed spaces of analytic functions, Complex Var. Theory Appl. 10(2–3) (1988), 115–122). We characterize the generators of these groups of isometries and also the spectrum of the generators. We provide an example on the Bloch space of an unbounded hermitian operator with non-compact resolvent.

Keywords

4647
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 3 , September 2014 , pp. 507 - 517
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

REFERENCES

1.Berkson, E. and Porta, H., Hermitian operators and one-parameter groups of isometries in Hardy spaces, Trans. Amer. Math. Soc. 185 (1973), 331–344.CrossRefGoogle Scholar
2.Cima, J. A. and Wogen, W. R., On isometries of the Bloch space, Illinois J. Math. 24 (2) (1980), 313–316.Google Scholar
3.Dunford, N. and Schwartz, J. T., Linear operators, part I (Interscience, New York, 1958)Google Scholar
4.Fleming, R. J. and Jamison, J. E., Hermitian operators and isometries on sums of Banach spaces, Proc. Edinburgh Math. Soc. 32 (2) (1989), 169–191.CrossRefGoogle Scholar
5.Forelli, F., The isometries of Hp, Can. J. Math. 16 (1964), 721–728.Google Scholar
6.Hille, E. and Phillips, R. S., Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31 (American Mathematical Society, Providence, RI, 1957).Google Scholar
7.Hornor, W. and Jamison, J. E., Isometries of some Banach spaces of analytic functions, Integral Equ. Operator Theory 41 (4) (2001), 410–425.Google Scholar
8.Kolaski, C. J., Isometries of some smooth normed spaces of analytic functions, Complex Var. Theory Appl. 10 (2–3) (1988), 115–122.Google Scholar
9.Li, S. and Stevic, S., Products of integral-type operators between Bloch spaces. J. Math. Anal. Appl. 349 (2009), 596–610.Google Scholar
10.Novinger, W. P. and Oberlin, D. M., Linear isometries of some normed spaces of analytic functions, Can. J. Math. 37 (1) (1985), 62–74.CrossRefGoogle Scholar
11.Palmer, T. W., Unbounded normal operators on Banach spaces, Trans. Amer. Math. Soc. 133 (1968), 385–414.Google Scholar
12.Vidav, I., Eine metrische Kennzeichnung der selbstadjungierten Operatoren, Math. Z. 66 (1956), 121–128.Google Scholar