2. Consider the following sequences in ¹. Determine which of them converges weakly and find the weak limits when they exist. a) (1, ..., 1, 0, ...). b) c) Xn = n In = (1,,,,, 0, ...). Τη Xn = (0, ..., 0, 1, 1, 0, ...0, ...). n
2. Consider the following sequences in ¹. Determine which of them converges weakly and find the weak limits when they exist. a) (1, ..., 1, 0, ...). b) c) Xn = n In = (1,,,,, 0, ...). Τη Xn = (0, ..., 0, 1, 1, 0, ...0, ...). n
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
2
![2. Consider the following sequences in l. Determine which of them
converges weakly and find the weak limits when they exist.
a)
(1, ., 1,0,..).
Xn =
b)
(1,
1 1
2' 3
0, ..).
Xn =
c) In =
(0,..., 0, 1, 1,0, ...0,...).
n
3. For which of the following space the unit ball is weakly compact
a) (²;
b) l';
c) C[0, 1];
d) l0;
e) L³[0, 1].
In each case explain your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e25041d-7573-46df-b9d3-ec2dd7694c16%2Ff1ad050e-f51a-4464-8084-e5011b1a3fdb%2F6g9ifgd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Consider the following sequences in l. Determine which of them
converges weakly and find the weak limits when they exist.
a)
(1, ., 1,0,..).
Xn =
b)
(1,
1 1
2' 3
0, ..).
Xn =
c) In =
(0,..., 0, 1, 1,0, ...0,...).
n
3. For which of the following space the unit ball is weakly compact
a) (²;
b) l';
c) C[0, 1];
d) l0;
e) L³[0, 1].
In each case explain your answer.
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