A Class of Contractions in Hilbert Space and Applications
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) no. 4, pp. 347-355.

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We characterize the bounded linear operators T in Hilbert space which satisfy T=βI+(1β)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 (Tn)n=1,2, by the continuous semigroup (et(IT))t0. Moreover, we give a stronger quadratic form inequality which ensures that sup{nTnTn+1:n=1,2,}. The results apply to large classes of Markov operators on countable spaces or on locally compact groups.
DOI : 10.4064/ba55-4-6
Mots-clés : characterize bounded linear operators hilbert space which satisfy beta beta where beta contraction characterizations include quadratic form inequality domination condition discrete semigroup ldots continuous semigroup t i t geq moreover stronger quadratic form inequality which ensures sup colon ldots infty results apply large classes markov operators countable spaces locally compact groups

Nick Dungey 1

1 Department of Mathematics Macquarie University Sydney, NSW 2109 Australia
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Nick Dungey. A Class of Contractions in Hilbert Space and Applications. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) no. 4, pp. 347-355. doi : 10.4064/ba55-4-6. https://geodesic-test.mathdoc.fr/articles/10.4064/ba55-4-6/

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