Radial Versus Othogonal and Minimal Projections onto Hyperplanes in l_4^3

• Main Author: Warner, Richard Alan
• Format: Others
• Published: Scholar Commons 2015
• Subjects: minimal projection; radial projection; norming functional; hyperplane; norming point; relative projection constant; hyperplane constant; Mathematics
• Online Access: http://scholarcommons.usf.edu/etd/5794; http://scholarcommons.usf.edu/cgi/viewcontent.cgi?article=6992&context=etd

In this thesis, we study the relationship between radial projections, and orthogonal and minimal projections in l_4^3. Specifically, we calculate the norm of the maximum radial projection and we prove that the hyperplane constant, with respect to the radial projection, is not achieved by a minimal projection in this space. We will also show our numerical results, obtained using computer software, and use them to approximate the norms of the radial, orthogonal, and minimal projections in l_4^3. Specifically, we show, numerically, that the maximum minimal projection is attained for ker{1,1,1} as well as compute the norms for the maximum radial and orthogonal projections.