Geodesic
UNBOUNDED HERMITIAN OPERATORS ON KOLASKI SPACES
Glasgow mathematical journal, Tome 56 (2014) no. 3, pp. 507-517

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.1017/S0017089513000426
Mots-clés : 46, 47 
JAMISON, JAMES; KING, RAENA. UNBOUNDED HERMITIAN OPERATORS ON KOLASKI SPACES. Glasgow mathematical journal, Tome 56 (2014) no. 3, pp. 507-517. doi: 10.1017/S0017089513000426
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[1] 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. Google Scholar | DOI

[2] 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] 3.Dunford, N. and Schwartz, J. T., Linear operators, part I (Interscience, New York, 1958) Google Scholar

[4] 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. Google Scholar | DOI

[5] 5.Forelli, F., The isometries of Hp, Can. J. Math. 16 (1964), 721–728. Google Scholar

[6] 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] 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] 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] 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] 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. Google Scholar | DOI

[11] 11.Palmer, T. W., Unbounded normal operators on Banach spaces, Trans. Amer. Math. Soc. 133 (1968), 385–414. Google Scholar

[12] 12.Vidav, I., Eine metrische Kennzeichnung der selbstadjungierten Operatoren, Math. Z. 66 (1956), 121–128. Google Scholar

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