Sale!

Functional Analysis  Homework 1

$30.00

Category:

Description

5/5 - (2 votes)

MATH4010 Functional Analysis
Homework 1

Notice:
• All the assignments must be submitted before the deadline.
• Each assignment should include your name and student ID number.
1. Show that
kxk =
Xn
k=0
sup
t∈[0,1]
|x
(k)
(t)| (1)
is a norm on C
n
[0, 1].
2. Let K be a compact topological space. Prove that the spaces C(K) with sup-norm and C
n
[0, 1]
with the norm defined in (1) are Banach spaces.
— THE END —
1