Optimization Seminar: Dr. Roman Sznajder
Bowie State University
Location
Mathematics/Psychology : 401
Date & Time
October 25, 2018, 10:30 am – 12:00 pm
Description
Title: Admission of a complex structure and complexification of Banach spaces. The story of restriction and extension of the field of scalars.
Speaker: Roman Sznajder
Abstract
In the class of real Banach spaces we discuss the problem of admission of a complex structure, that is, given a real B-space F we try to find a real-linear isomorphism of F onto a complex B-space E. We give a characterization of such spaces F. In particular cases, there may exist such a complex B-space E, so that F is obtained from E by a mere restriction of its field of complex scalars to the field of reals. We will also discuss the converse problem of constructing (for a given real B-space F) a complex B-space E by extension of the field of reals - the so-called complexification problem. We provide a characterization of those complex B-spaces which are isomorphic to the complexification of a real B-space.
Speaker: Roman Sznajder
Abstract
In the class of real Banach spaces we discuss the problem of admission of a complex structure, that is, given a real B-space F we try to find a real-linear isomorphism of F onto a complex B-space E. We give a characterization of such spaces F. In particular cases, there may exist such a complex B-space E, so that F is obtained from E by a mere restriction of its field of complex scalars to the field of reals. We will also discuss the converse problem of constructing (for a given real B-space F) a complex B-space E by extension of the field of reals - the so-called complexification problem. We provide a characterization of those complex B-spaces which are isomorphic to the complexification of a real B-space.
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