A class of contractions in Hilbert space and applications

• Autorzy: Dungey N.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

contraction operator; Hilbert space; Markov operator; convolution operator

PL

przestrzeń Hilberta; operator Markowa

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2007
• Tom: Vol. 55, no 2
• Strony: 347--355
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Dungey N.

• Department of Mathematics, Macquarie University, Sydney, NSW 2109 Australia,

Bibliografia

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