Consider a linear functional T: C[0, 1] → C, defined for every fe C[0, 1] by T(f) = f(1). Show that T is continuous in C[0, 1] with respect to the supremum norm ||f|| sup f(t)\. te [0,1]
Consider a linear functional T: C[0, 1] → C, defined for every fe C[0, 1] by T(f) = f(1). Show that T is continuous in C[0, 1] with respect to the supremum norm ||f|| sup f(t)\. te [0,1]
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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![Consider a linear functional T: C[0, 1] → C, defined for every fe C[0, 1] by T(f) = ƒ(1).
Show that T is continuous in C[0, 1] with respect to the supremum norm
||f||=
=
sup f(t)\.
te [0,1]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad5d73be-1e36-4921-8501-b71214c2b59c%2Ffb0bf146-84d4-4582-b37e-121012d362e3%2Fwk30m1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider a linear functional T: C[0, 1] → C, defined for every fe C[0, 1] by T(f) = ƒ(1).
Show that T is continuous in C[0, 1] with respect to the supremum norm
||f||=
=
sup f(t)\.
te [0,1]
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