Show that the operator K: L²[0, 1] → L²[0, 1] given by K f(x) = f f(y) √x+y x = [0, 1] is compact.
Show that the operator K: L²[0, 1] → L²[0, 1] given by K f(x) = f f(y) √x+y x = [0, 1] is compact.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 5E: 5. Prove that the equation has no solution in an ordered integral domain.
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![Show that the operator K: L²[0, 1] → L²[0, 1] given by
Kf(x) = f
= 1²
x = [0, 1]
is compact.
f(y)
√x+y'](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7a159ee-ed17-4137-bfca-c0c828eb7e35%2F2cac49ed-861d-482e-a39f-65d9eecd336f%2Fr76m66b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Show that the operator K: L²[0, 1] → L²[0, 1] given by
Kf(x) = f
= 1²
x = [0, 1]
is compact.
f(y)
√x+y'
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