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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

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1072-947X
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Volume 19, Issue 2

Issues

Complexifications of real spaces: General aspects

María Elena Luna-Elizarrarás
  • Departamento de Matemáticas, Escuela Superior de Física y Matemáticas, del Instituto Politécnico Nacional, Mexico City, Mexico
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/ Francisco Ramírez-Reyes
  • Departamento de Matemáticas, Escuela Superior de Física y Matemáticas, del Instituto Politécnico Nacional, Mexico City, Mexico
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/ Michael Shapiro
  • Departamento de Matemáticas, Escuela Superior de Física y Matemáticas, del Instituto Politécnico Nacional, Mexico City, Mexico
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Published Online: 2012-05-30 | DOI: https://doi.org/10.1515/gmj-2012-0013

Abstract.

Linear spaces are considered in the following four situations: a real space admits multiplication by complex scalars without changing the set itself; a real space is embedded into a wider set with multiplication by complex scalars; a complex space has an involution and thus has “real” and “imaginary” elements; a combination of the previous ones. We study how they manifest themselves when the initial space possesses additional structures such as topology, norm, inner product, and also the behavior of linear operators between such spaces.

Keywords: Complexification of real spaces; involutions on complex spaces; Banach space; Hilbert space

About the article

Received: 2011-05-23

Published Online: 2012-05-30

Published in Print: 2012-06-01


Citation Information: Georgian Mathematical Journal, Volume 19, Issue 2, Pages 259–282, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2012-0013.

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