Answered: Let L and M be two continuous linear…

Let L and M be two continuous linear maps such that the composite Mo L is defined. By quoting appropriate theorems show that MoL is a continuous linear map and prove that ||M o L|| < ||M|||L||.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 27E: 27. Let , where and are nonempty. Prove that has the property that for every subset of if and...

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Question

Let L and M be two continuous linear maps such that the composite Mo L
is defined. By quoting appropriate theorems show that M oL is a continuous
linear map and prove that
||M o L|| < || M|||L||.
Prove the following statement:
If LE L(R", R") with matrix given by
a11
a12
alm
[L] =
Anl
an2
anm
...
n
n
then | L < ΣΣας.
i=1 j=1

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