MIT OpenCourseWarehttp://ocw.mit.edu 18.102 Introduction to Functional Analysis Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.7 LECTURE NOTES FOR 18.102, SPRING 2009 Lecture 2. Thursday, 5 Feb. Plan:- Linear maps between normed spaces are continuous iff they are bounded. The best bound gives a norm. If the second space is Banach the space of linear operators is Banach. Corollary – the dual space of a normed space is a Banach space. Examples: Integral operators on C0([0, 1]) with respect to supremum or L1 norms. Differentiation as an operator from C1([0, 1]) to C0([0, 1]) In practice:- I did not get to the part about differentiation. Reading: (1) Wilde:- Chapter 2 to 2.7 (2) Chen:- First part of Chapter 6 and of Chapter 7. (3) Ward:- Chapter 3, first 2
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