2. Recall that coo denotes the finite sequence space which is equipped with the || ||1-norm. Let T Coo Coo be the linear map given by T(x)(k) := kx(k) for k 1,2... and x = Coo. Show that T is a discontinuous map. ==

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 23E
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2. Recall that coo denotes the finite sequence space which is equipped with the || ||1-norm.
Let T Coo Coo be the linear map given by
T(x)(k) := kx(k)
for k 1,2... and x = Coo. Show that T is a discontinuous map.
==
Transcribed Image Text:2. Recall that coo denotes the finite sequence space which is equipped with the || ||1-norm. Let T Coo Coo be the linear map given by T(x)(k) := kx(k) for k 1,2... and x = Coo. Show that T is a discontinuous map. ==
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