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Suppose X and Y are normed spaces and X + 0. Prove that BL(X, Y) is a Banach space with the operator norm if and only if Y is a Banach space.

Suppose X and Y are normed spaces and X + 0. Prove that BL(X, Y) is a Banach space with the operator norm if and only if Y is a Banach space.

Advanced Engineering Mathematics
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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Suppose X and Y are normed spaces and X + 0. Prove that BL(X, Y) is a Banach space with the operator norm if and only if Y is a Banach space.
Transcribed Image Text:Suppose X and Y are normed spaces and X + 0. Prove that BL(X, Y) is a Banach space with the operator norm if and only if Y is a Banach space.
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