← Back to Event List

Optimization Seminar: Dr. Roman Sznajder

Bowie State University

Location

Mathematics/Psychology : 401

Date & Time

October 25, 2018, 10:30 am12:00 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.