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Abstract and Applied Analysis
Volume 2013, Article ID 380475, 8 pages
Research Article

Generalized Numerical Index and Denseness of Numerical Peak Holomorphic Functions on a Banach Space

1Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of Korea
2Department of Mathematics Education, Dongguk University-Seoul, Seoul 100-715, Republic of Korea

Received 11 June 2013; Accepted 23 August 2013

Academic Editor: Geraldo Botelho

Copyright © 2013 Sung Guen Kim and Han Ju Lee. 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.


The generalized numerical index of a Banach space is introduced, and its properties on certain Banach spaces are studied. Ed-dari's theorem on the numerical index is extended to the generalized index and polynomial numerical index of a Banach space. The denseness of numerical strong peak holomorphic functions is also studied.