TY - JOUR
T1 - Complexifications of real spaces
T2 - General aspects
AU - Luna-Elizarrarás, María Elena
AU - Ramírez-Reyes, Francisco
AU - Shapiro, Michael
N1 - Funding Information:
Research was partially supported by CONACYTprojects as well as by Instituto Politécnico Nacional in the framework of its COFAA and SIP programs and by COFAA-IPN.
PY - 2012/6
Y1 - 2012/6
N2 - 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.
AB - 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.
KW - Banach space
KW - Complexification of real spaces
KW - Hilbert space
KW - Involutions on complex spaces
UR - http://www.scopus.com/inward/record.url?scp=84870328244&partnerID=8YFLogxK
U2 - 10.1515/gmj-2012-0013
DO - 10.1515/gmj-2012-0013
M3 - Artículo
SN - 1072-947X
VL - 19
SP - 259
EP - 282
JO - Georgian Mathematical Journal
JF - Georgian Mathematical Journal
IS - 2
ER -