Inequalities of Hlawka type for matrices

Authors
Citation
S. Wada, Inequalities of Hlawka type for matrices, ARCH MATH, 77(5), 2001, pp. 415-422
Citations number
8
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
ARCHIV DER MATHEMATIK
ISSN journal
0003-889X → ACNP
Volume
77
Issue
5
Year of publication
2001
Pages
415 - 422
Database
ISI
SICI code
0003-889X(20011101)77:5<415:IOHTFM>2.0.ZU;2-2
Abstract
A generalized Hlawka's inequality says that for any n (greater than or equa l to 2) complex numbers x(1), x(2),...,x(n), Sigma (n)(i=1)\x(i) - Sigma (n)(j=1) x(j)\ less than or equal to Sigma (n)( i=1) \x(i)\ + (n-2)\ Sigma (n)(j=1)x(j)\. We generalize this inequality to the trace norm and the trace of an n x n m atrix A as parallel toA - TrA parallel to (1) less than or equal to parallel toA paral lel to (1) + (n-2)\ TrA \. We consider also the related inequalities for p-norms (1 less than or equal to p less than or equal to infinity) on matrices.