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Complexifications of real spaces: General aspects
-
María Elena Luna-Elizarrarás
,
Francisco Ramírez-Reyes
Published/Copyright:
May 30, 2012
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
Received: 2011-05-23
Published Online: 2012-05-30
Published in Print: 2012-June
© 2012 by Walter de Gruyter Berlin Boston
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Keywords for this article
Complexification of real spaces;
involutions on complex spaces;
Banach space;
Hilbert space
Articles in the same Issue
- Masthead
- Boundedness of the parametric Marcinkiewicz integral operator and its commutators on generalized Morrey spaces
- Modules that have a supplement in every cofinite extension
- Boundary value problems of statics of the elastic mixture theory
- On grand Lorentz spaces and the maximal operator
- Measurable and nonmeasurable sets with homogeneous sections
- Complexifications of real spaces: General aspects
- Continuous Hu cohomology
- Convergence and existence results for best C-proximity points
- Aspects of slice stability in locale theory
- On the irreducibility of Hurwitz spaces of coverings with two special fibers
- Weighted composition followed by differentiation between weighted Banach spaces of holomorphic functions
