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Complex Structures and Conjugations

Wettersten, Zenny LU (2022) In Master’s Theses in Mathematical Sciences MATM03 20222
Mathematics (Faculty of Sciences)
Centre for Mathematical Sciences
Abstract
An introductory analysis of complex conjugation operators and complex structures is presented. We show that complex structures can be constructed on a real vector space V if V is the direct sum of two isomorphic subspaces, and relate this to the existence of a well-defined conjugation operator. Additionally, it is shown that all complex structures on a vector space V are similar operators. Some applications to different subjects, e.g. functional analysis, are showcased.
Please use this url to cite or link to this publication:
author
Wettersten, Zenny LU
supervisor
organization
course
MATM03 20222
year
type
H2 - Master's Degree (Two Years)
subject
keywords
complex structures, conjugations, complex vector spaces, complexification, linear algebra, set theory
publication/series
Master’s Theses in Mathematical Sciences
report number
LUNFMA-3132-2022
ISSN
1404-6342
other publication id
2022:E66
language
English
id
9102499
date added to LUP
2025-10-02 16:31:42
date last changed
2025-10-02 16:31:42
@misc{9102499,
  abstract     = {{An introductory analysis of complex conjugation operators and complex structures is presented. We show that complex structures can be constructed on a real vector space V if V is the direct sum of two isomorphic subspaces, and relate this to the existence of a well-defined conjugation operator. Additionally, it is shown that all complex structures on a vector space V are similar operators. Some applications to different subjects, e.g. functional analysis, are showcased.}},
  author       = {{Wettersten, Zenny}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master’s Theses in Mathematical Sciences}},
  title        = {{Complex Structures and Conjugations}},
  year         = {{2022}},
}