Abstract
The study begun in [3]is continued. Namely the modified unilateral translation part, which appears in the Wold-type decomposition given in [3], is characterized. The ultraevanescent part, i.e., the orthocomplement of both (unilateral and modified unilateral) translation parts, is also considered. Finally, conditions on self-duality of isometric semigroups in terms of unilateral, modified unilateral translation and ultraevanescent semigroups are discussed.
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References
Conway, J.B., The dual of a subnormal operator. J. Operator Theory 5, 2(1981), 195–211.
Douglas, R.G., On extending commutative semigroups of isometries. Bull. London Math.Soc. 1(1969), 157–159.
Gaşpar, D., — Suciu, N., On the structure of isometric semigroups. Proceedings of the 8th Conference of Operator Theory, Timişoara and Herculane, June 6–16, 1983 (in print).
Helson, H. — Lowdenslager, D., Prediction theory and Fourier series in several variables II. Acta Math. 106(1961), 175–213.
Ito, T., On the commutative family of subnormal operators. J.Faculty Sci. Hokkaido Univ., Ser.I Math. 14(1958), 1–15.
Muhly, P.S., A structure theory for isometric representations of a class of semigroups. J. Reine Angew.Math. 225(1972), 135–154.
Suciu, I., On the semi-groups of isometries. Studia Math.(PAN) 30(1968), 101–110.
Suciu, I., Function Algebras. Ed.Academiei R.S.R., Bucuresti, 1973.
Sz.-Nagy, B. – Foiaj, C, Harmonic Analysis of Operators on Hilbert space. North-Holland Publishing Company, Amsterdam/London, 1974.
Wold, H., A study in the analysis of stationary time series. Uppsala, Stockholm, 1938.
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© 1984 Springer Basel AG
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Gaşpar, D., Suciu, N. (1984). On the Wold Decomposition of Isometric Semigroups. In: Butzer, P.L., Stens, R.L., Sz.-Nagy, B. (eds) Anniversary Volume on Approximation Theory and Functional Analysis. ISNM 65: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 65. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5432-0_10
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DOI: https://doi.org/10.1007/978-3-0348-5432-0_10
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