Abstract
This survey article contains the lecture delivered on the conference; it is based on the papers [5]– [9], where complete proofs can be found. In the first section we present results concerning single operators, and the second section is devoted to the study of representations of general discrete abelian semigroups. The main idea in both sections is to apply an appropriate normalizing gauge function in order to get connection with an isometry, or isometric representation.
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References
C. J. K. Batty and Q. P. Vũ, Stability of strongly continuous representations of abelian semigroups Math. Z., 209 (1992), 75–88.
H. Bercovici, Commuting power bounded operators Acta Sci. Math. (Szeged), 57 (1993), 55–64.
M. M. Day, Ergodic theorems for abelian semigroups Trans. Amer. Math. Soc., 51 (1942), 399–412.
L. Kérchy, Isometric asymptotes of power bounded operatorsIndiana Univ. Math. J., 38 (1989), 173–188.
L. Kérchy, Operators with regular norm-sequences Acta Sci. Math. (Szeged), 63 (1997), 571–605.
L. Kérchy, Hyperinvariant subspaces of operators with non-vanishing orbits Proc.Amer.Math. Soc., 127 (1999), 1363–1370.
L. Kérchy, Criteria of regularity for norm-sequences Integral Equations Operator Theory, to appear.
L. Kérchy and V. Müller, Criteria of regularity for norm-sequences. II Acta Sci.Math. (Szeged), to appear.
L. Kérchy, Representations with regular norm-behaviour of discrete abelian semigroups, submitted to Acta Sci. Math. (Szeged).
G. G. Lorentz, A contribution to the theory of divergent sequences Acta Math., 80 (1948), 167–190.
Y.I. Lyubich, Introduction to the theory of Banach representations of groups OT 30, Birkhäuser, Basel-Boston—Berlin, 1988.
B. Sz.-Nagy, On uniformly bounded linear transformations in Hilbert space Acta Sci. Math. (Szeged), 11 (1947), 152–157.
B. Sz.-Nagy and C. Foias, Harmonic Analysis of Operators on Hilbert Space North Holland - Akadémiai Kiadó, Amsterdam - Budapest, 1970.
Q. P. Vũ, Theorems of Katznelson-Tzafriri type for semigroups of operators J. Funct. Anal., 103 (1992), 74–84.
Q. P. Vũ, Almost periodic and strongly stable semigroups of operators Banach Center Publ. 38, Warsaw, 1994, 401–426.
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Kérchy, L. (2000). Unbounded Representations of Discrete Abelian Semigroups. In: Balakrishnan, A.V. (eds) Semigroups of Operators: Theory and Applications. Progress in Nonlinear Differential Equations and Their Applications, vol 42. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8417-4_13
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DOI: https://doi.org/10.1007/978-3-0348-8417-4_13
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