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We characterize the bounded linear operators T in Hilbert space which satisfy T = βI + (1 - β)S where β ∈ (0,1) and S is a contraction. The characterizations include a quadratic form inequality, and a domination condition of the discrete semigroup (T[sup]n)n=1,2,... by the continuous semigroup (e[sup]-t(I-T)t≥o. Moreover, we give a stronger quadratic form inequality which ensures that sup{n||T[sup]n - T[sup]n+1 ||: n = 1, 2,...} < ∞. The results apply to large classes of Markov operators on countable spaces or on locally compact groups.
Wydawca
Rocznik
Tom
Strony
347--355
Opis fizyczny
Bibliogr. 13 poz.
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autor
- Department of Mathematics, Macquarie University, Sydney, NSW 2109 Australia, ndungey@ics.mq.edu.au
Bibliografia
- [1] S. Blunck, Perturbation of analytic operators and temporal regularity of discrete heat kernels, Colloq. Math. 86 (2000), 189-201.
- [2] —, Analyticity and discrete maximal regularity on Lp-spaces, J. Funct. Anal. 183(2001), 211-230.
- [3] T. Coulhon, A. Grigor'yan and F. Zucca, The discrete integral maximum principle and its applications, Tohoku Math. J. 57 (2005), 559-587.
- [4] N. Dungey, A note on time regularity for discrete time heat kernels, Semigroup Forum 72 (2006), 404-410.
- [5] —, Time regularity for random walks on locally compact groups, Probab. Theory Related Fields 137 (2007), 429-442.
- [6] —, On time regularity and related conditions for power-bounded operators, Proc. London Math. Soc., to appear.
- [7] N. Kalton, S. Montgomery-Smith, K. Oleszkiewicz and Y. Tomilov, Power-bounded operators and related norm estimates, J. London Math. Soc. 70 (2004), 463-478.
- [8] T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Grundlehren Math.Wiss. 132, Springer, 1980.
- [9] O. Nevanlinna, Convergence of Iterations for Linear Equations, Birkhauser, Basel,1993.
- [10] —, On the growth of the resolvent operators for power-bounded operators, in: Linear Operators, J. Janas et al. (eds.), Banach Center Publ. 38, Inst. Math., Polish Acad. Sci., 1997, 247-264.
- [11] —, Resolvent conditions and powers of operators, Studia Math. 145 (2001), 113-134.
- [12] N. T. Varopoulos, L. Saloff-Coste and T. Coulhon, Analysis and Geometry on Groups, Cambridge Tracts in Math. 100, Cambridge Univ. Press, 1992.
- [13] K. Yosida, Functional Analysis, 6th ed., Grundlehren Math. Wiss. 123, Springer, 1980.
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Bibliografia
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bwmeta1.element.baztech-article-BAT5-0024-0074