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Math Colloquium: Complexifications and Isometries
Start Date: 11/13/2019Start Time: 3:00 PM
End Date: 11/13/2019End Time: 4:00 PM

Event Description

Edward Poon, Embry-Riddle Aeronautical University

Abstract: Given a norm $\| \cdot \|$ on a real Banach space $X$, there is a smallest ‘reasonable’ complexification norm $\| \cdot \|_C$ on the complexified space $X_C$, defined by $$\| x+ iy \|_C = \sup \{\|x \cos \theta + y \sin \theta \| : \theta \in [0, 2\pi]\}$$ for $x,y \in X$. Provided $X$ has a certain finiteness condition (possessed by all finite-dimensional spaces) we characterize the isometries for $\| \cdot \|_C$ in terms of the isometries for $\| \cdot \|$.

Contact Information:
Name: Georgi Medvedev
Email: gsm29@drexel.edu
Korman Center, Room 243, 15 S. 33rd Street, Philadelphia, PA 19014
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