Numerical radius inequalities for Hilbert space operators

Fuad Kittaneh. "Numerical radius inequalities for Hilbert space operators." Studia Mathematica 168.1 (2005): 73-80. <http://eudml.org/doc/284514>.

@article{FuadKittaneh2005,
abstract = { It is shown that if A is a bounded linear operator on a complex Hilbert space, then 1/4 ||A*A + AA*|| ≤ (w(A))² ≤ 1/2 ||A*A + AA*||, where w(·) and ||·|| are the numerical radius and the usual operator norm, respectively. These inequalities lead to a considerable improvement of the well known inequalities 1/2 ||A|| ≤ w(A) ≤ || A||. Numerical radius inequalities for products and commutators of operators are also obtained. },
author = {Fuad Kittaneh},
journal = {Studia Mathematica},
keywords = {numerical radius; operator norm; Cauchy-Schwarz inequality; commutator},
language = {eng},
number = {1},
pages = {73-80},
title = {Numerical radius inequalities for Hilbert space operators},
url = {http://eudml.org/doc/284514},
volume = {168},
year = {2005},
}

TY - JOUR
AU - Fuad Kittaneh
TI - Numerical radius inequalities for Hilbert space operators
JO - Studia Mathematica
PY - 2005
VL - 168
IS - 1
SP - 73
EP - 80
AB - It is shown that if A is a bounded linear operator on a complex Hilbert space, then 1/4 ||A*A + AA*|| ≤ (w(A))² ≤ 1/2 ||A*A + AA*||, where w(·) and ||·|| are the numerical radius and the usual operator norm, respectively. These inequalities lead to a considerable improvement of the well known inequalities 1/2 ||A|| ≤ w(A) ≤ || A||. Numerical radius inequalities for products and commutators of operators are also obtained.
LA - eng
KW - numerical radius; operator norm; Cauchy-Schwarz inequality; commutator
UR - http://eudml.org/doc/284514
ER -