A Class of Contractions in Hilbert Space and Applications

• Autorzy: Nick Dungey
• 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 $(Tⁿ)_{n=1,2,...}$ by the continuous semigroup $(e^{-t(I-T)})_{t≥0}$. Moreover, we give a stronger quadratic form inequality which ensures that $sup {n∥Tⁿ - T^{n+1}∥: n = 1,2,...} < ∞$. The results apply to large classes of Markov operators on countable spaces or on locally compact groups.

Kategorie tematyczne

• 47A30: Norms (inequalities, more than one norm, etc.)
• 60G15: Gaussian processes
• 60G50: Sums of independent random variables; random walks
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2007
• Tom: 55
• Numer: 4
• Strony: 347-355

Daty

wydano

2007

Twórcy

autor

Nick Dungey

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

Identyfikatory

DOI

10.4064/ba55-4-6