Bounded Linear Transformations
Nonlinear analysis studies functions on normed linear spaces and, if all those functions were linear, the subject wouldn’t have that name. But some of the functions we study are linear, and there is a branch of mathematics, functional analysis, that can tell us a lot about such linear functions. This book contains one substantial topic from functional analysis, the spectral theory of compact linear operators, that is presented in detail in Chapter 15. As background to that chapter, and for several other topics, we need the facts about linear transformations that I have collected here. Everything in this appendix can be found in textbooks of functional analysis. But those books are long and this appendix is short so, if you don’t already know these things, you’ll find it a bit easier to locate them here. I’ll assume that you are looking up these facts to support what is in the text and therefore you’ll know from the text what the words and symbols mean.
KeywordsBanach Space Functional Analysis Linear Transformation Unit Ball Open Mapping
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