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Journal of Function Spaces
Volume 2016 (2016), Article ID 5240218, 7 pages
http://dx.doi.org/10.1155/2016/5240218
Research Article

Matrix Quasinorms Induced by Maximal and Minimal Vector Norms

Department of Mathematics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Republic of Korea

Received 6 July 2016; Accepted 28 September 2016

Academic Editor: Hans G. Feichtinger

Copyright © 2016 Jong-Do Park. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In the set of all vector norms in , there exist maximal and minimal complex norms which coincide with the real Euclidean norm in . The purpose of this paper is to introduce new quasinorms defined on complex matrices. These two matrix quasinorms are induced by maximal and minimal complex vector norms. We also prove the dual relation between these two quasinorms.