2006/08/07 by Gautam Bharali, Bharali, Gautam
Mathematics · #30C80 #32F45 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:30C80 #msc:32F45
paper · pdf · doi:10.48550/arxiv.math/0608177
8 pages
arxiv created 2006/08/07 · arxiv updated 2009/12/01
We provide generalisations of two Schwarz-type lemmas -- the first a result of Globevnik and the other due to Ransford and White -- for holomorphic mappings into the spectral unit ball. The first concerns mappings of the unit disc in C into the spectral unit ball, while the second concerns self- mappings. The aforementioned results apply to holomorphic mappings that map the origin to the origin. We extend these results to general holomorphic mappings into the spectral unit ball. We also show that our results are sharp.