1. Consider the space of absolutely convergent sequences equipped with the following norm 1/2 || (21, ..., In, ...) ||1,2= #;\ + ( 2 I;1² (0.1) j=1 j=1 a). Prove that || · ||1.2 is a norm.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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1. Consider the space of absolutely convergent sequences equipped
with the following norm
1/2
(0.1)
j=1
j=1
a). Prove that || · ||1.2 is a norm.
b). Is this norm equivalent to the standard || x ||1=E, x;|?
!!
1/2
c). Is it equivalent to || ||2= ( E ®
Transcribed Image Text:1. Consider the space of absolutely convergent sequences equipped with the following norm 1/2 (0.1) j=1 j=1 a). Prove that || · ||1.2 is a norm. b). Is this norm equivalent to the standard || x ||1=E, x;|? !! 1/2 c). Is it equivalent to || ||2= ( E ®
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