On the norms of quaternionic extensions of real and complex linear mappings

Daniel Alpay; M. Elena Luna-Elizarrarás; Michael Shapiro

doi:10.1002/mma.822

On the norms of quaternionic extensions of real and complex linear mappings

Daniel Alpay
, M. Elena Luna-Elizarrarás
, Michael Shapiro

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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 /t-linear mappings are defined for the quaternionic case, are considered too.

Original language	English
Pages (from-to)	1005-1036
Number of pages	32
Journal	Mathematical Methods in the Applied Sciences
Volume	30
Issue number	9
DOIs	https://doi.org/10.1002/mma.822
State	Published - 1 Jun 2007

Keywords

Norms of quaternionic extensions
Quaternionic linear operators

ASJC Scopus subject areas

General Mathematics
General Engineering

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10.1002/mma.822

Cite this

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abstract = "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 /t-linear mappings are defined for the quaternionic case, are considered too.",

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AU - Alpay, Daniel

AU - Luna-Elizarrarás, M. Elena

AU - Shapiro, Michael

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Y1 - 2007/6/1

N2 - 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 /t-linear mappings are defined for the quaternionic case, are considered too.

AB - 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 /t-linear mappings are defined for the quaternionic case, are considered too.

KW - Norms of quaternionic extensions

KW - Quaternionic linear operators

UR - https://www.scopus.com/pages/publications/34249330264

U2 - 10.1002/mma.822

DO - 10.1002/mma.822

M3 - Article

AN - SCOPUS:34249330264

SN - 0170-4214

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JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 9

ER -

On the norms of quaternionic extensions of real and complex linear mappings

Abstract

Keywords

ASJC Scopus subject areas

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