*This preview shows
page 1. Sign up
to
view the full content.*

**Unformatted text preview: **b) Show that I is a bounded operator, that is, there exists a number B so that k If k B k f k for all f C [0 , 2] and nd the (smallest) number B . 3. Consider the dierentiation operator D : P P (acting on polyno-mials): Df = df dt a) Show that D is a linear transformation. b) Equip P with the sup norm on [0 , 2]. Show that D is an unbounded operator: consider the polynomials f n ( t ) = t n and show that there is no constant B so that k Df n k B k f n k for all n . 1...

View
Full
Document