A Class of Contractions in Hilbert Space and Applications

Nick Dungey

Bulletin of the Polish Academy of Sciences. Mathematics (2007)

  • Volume: 55, Issue: 4, page 347-355
  • ISSN: 0239-7269

Abstract

top
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 ) n = 1 , 2 , . . . by the continuous semigroup ( e - t ( I - T ) ) t 0 . Moreover, we give a stronger quadratic form inequality which ensures that s u p n T - T n + 1 : n = 1 , 2 , . . . < . The results apply to large classes of Markov operators on countable spaces or on locally compact groups.

How to cite

top

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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.