TY - JOUR
T1 - On Complexification of Real Spaces and its Manifestations in the Theory of Bochner and Pettis Integrals
AU - Luna-Elizarrarás, M. E.
AU - Ramírez-Reyes, F.
AU - Shapiro, M.
N1 - Publisher Copyright:
© 2022, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2022/7
Y1 - 2022/7
N2 - This work is a continuation of our work [14] where we considered linear spaces in the following two situations: a real space admits a multiplication by complex scalars without changing the set itself; a real space is embedded into a wider set with a multiplication by complex scalars. We studied there also how they manifest themselves when the initial space possesses additional structures: topology, norm, inner product, as well as what happens with linear operators acting between such spaces. Changing the linearities of the linear spaces unmasks some very subtle properties which are not thus obvious when the set of scalars is not changed. In the present work we follow the same idea considering now Bochner and Pettis integrals for functions ranged in real and complex Banach and Hilbert spaces. Finally, this leads to the study of strong and weak random elements with values in real and complex Banach and Hilbert spaces, in particular, some properties of their expectations.
AB - This work is a continuation of our work [14] where we considered linear spaces in the following two situations: a real space admits a multiplication by complex scalars without changing the set itself; a real space is embedded into a wider set with a multiplication by complex scalars. We studied there also how they manifest themselves when the initial space possesses additional structures: topology, norm, inner product, as well as what happens with linear operators acting between such spaces. Changing the linearities of the linear spaces unmasks some very subtle properties which are not thus obvious when the set of scalars is not changed. In the present work we follow the same idea considering now Bochner and Pettis integrals for functions ranged in real and complex Banach and Hilbert spaces. Finally, this leads to the study of strong and weak random elements with values in real and complex Banach and Hilbert spaces, in particular, some properties of their expectations.
UR - http://www.scopus.com/inward/record.url?scp=85135283599&partnerID=8YFLogxK
U2 - 10.1007/s10958-022-06034-0
DO - 10.1007/s10958-022-06034-0
M3 - Artículo
AN - SCOPUS:85135283599
SN - 1072-3374
VL - 264
SP - 768
EP - 781
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
IS - 6
ER -