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On the norms of quaternionic extensions of real and complex linear mappings
Author(s) -
Alpay Daniel,
LunaElizarrarás M. Elena,
Shapiro Michael
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.822
Subject(s) - mathematics , bounded function , complexification , pure mathematics , space (punctuation) , linear operators , quaternionic representation , range (aeronautics) , normed vector space , algebra over a field , product (mathematics) , linear map , mathematical analysis , geometry , computer science , materials science , composite material , irreducible representation , real representation , operating system
We study the connections between the norms of bounded operators on real and complex normed spaces, and with range in quaternionic spaces, and of their quaternionic extensions. We study some aspects of the relations between the quaternionization and the complexification of an inner product real space. The problems that arise when k ‐linear mappings are defined for the quaternionic case, are considered too. Copyright © 2006 John Wiley & Sons, Ltd.