A Class of Contractions in Hilbert Space and Applications
Nick Dungey
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007), p. 347-355 / Harvested from The Polish Digital Mathematics Library
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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 (Tⁿ)n=1,2,... by the continuous semigroup (e-t(I-T))t≥0. Moreover, we give a stronger quadratic form inequality which ensures that supn∥Tⁿ-Tn+1∥:n=1,2,...<∞. The results apply to large classes of Markov operators on countable spaces or on locally compact groups.

Publié le : 2007-01-01
EUDML-ID : urn:eudml:doc:281234 
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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) pp. 347-355. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-4-6/