Title : ( SCHATTEN p–NORM INEQUALITIES RELATED TO A CHARACTERIZATION OF INNER PRODUCT SPACES )
Authors: O. Hirzallah , F. Kittaneh , Mohammad Sal Moslehian ,
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Abstract
Let A1, ···An be operators acting on a separable complex Hilbert space such that ∑n i=1 Ai = 0. It is shown that if A1, ···An belong to a Schatten p-class, for some p > 0, then 2p/2np−1 n ∑ i=1Aip p n ∑ i, j=1Ai ±Ajp p for 0 < p 2, and the reverse inequality holds for 2 p < ∞ . Moreover, n ∑ i, j=1Ai ±Aj2 p 2n2/p n ∑ i=1Ai2 p for 0 < p 2, and the reverse inequality holds for 2 p < ∞ . These inequalities are related to a characterization of inner product spaces due to E.R. Lorch.
Keywords
, Schatten p-norm, positive operator, inequality, inner product space.
@article{paperid:1015072,
author = {O. Hirzallah and F. Kittaneh and Sal Moslehian, Mohammad},
title = {SCHATTEN p–NORM INEQUALITIES RELATED TO A CHARACTERIZATION OF INNER PRODUCT SPACES},
journal = {Mathematical Inequalities and Applications},
year = {2010},
volume = {13},
number = {2},
month = {May},
issn = {1331-4343},
pages = {235--241},
numpages = {6},
keywords = {Schatten p-norm; positive operator; inequality; inner product space.},
}
%0 Journal Article
%T SCHATTEN p–NORM INEQUALITIES RELATED TO A CHARACTERIZATION OF INNER PRODUCT SPACES
%A O. Hirzallah
%A F. Kittaneh
%A Sal Moslehian, Mohammad
%J Mathematical Inequalities and Applications
%@ 1331-4343
%D 2010
