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# Math Colloquium: Complexifications and Isometries

Wednesday, November 13, 2019

3:00 PM-4:00 PM

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 $\| \cdot \|$.

Georgi Medvedev
gsm29@drexel.edu

## Location

Korman Center, Room 243, 15 S. 33rd Street, Philadelphia, PA 19014

• Everyone