A Class of Contractions in Hilbert Space and Applications

Nick Dungey. "A Class of Contractions in Hilbert Space and Applications." Bulletin of the Polish Academy of Sciences. Mathematics 55.4 (2007): 347-355. <http://eudml.org/doc/281234>.

@article{NickDungey2007,
abstract = {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.},
author = {Nick Dungey},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {contraction operator; Hilbert space; Markov operator; convolution operator},
language = {eng},
number = {4},
pages = {347-355},
title = {A Class of Contractions in Hilbert Space and Applications},
url = {http://eudml.org/doc/281234},
volume = {55},
year = {2007},
}

TY - JOUR
AU - Nick Dungey
TI - A Class of Contractions in Hilbert Space and Applications
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2007
VL - 55
IS - 4
SP - 347
EP - 355
AB - 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.
LA - eng
KW - contraction operator; Hilbert space; Markov operator; convolution operator
UR - http://eudml.org/doc/281234
ER -