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(a) Define a reflexive space. Prove that a Banach space is reflexive if and only if its dual space is reflexive. (b) State closed graph theorem. Deduce open mapping theorem from the closed graph theorem.

(a) Define a reflexive space. Prove that a Banach space is reflexive if and only if its dual space is reflexive. (b) State closed graph theorem. Deduce open mapping theorem from the closed graph theorem.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please answer both subparts a and b with all the required steps

(a) Define a reflexive space. Prove that a Banach space is reflexive if and only if its dual space is reflexive. (b) State closed graph theorem. Deduce open mapping theorem from the closed graph theorem. 2.
Transcribed Image Text:(a) Define a reflexive space. Prove that a Banach space is reflexive if and only if its dual space is reflexive. (b) State closed graph theorem. Deduce open mapping theorem from the closed graph theorem. 2.
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