Lec - 10 Continuous (Bounded) Transformation In Normed Space | Important Theorems on Continuity

Lec - 10 Continuous (Bounded) Transformation In Normed Space | Important Theorems on Continuity

Welcome to my YouTube Channel Excellence Learning

What you will learn In this video 👇

1) Definition of Linear Transformation
2) Definition of Continuous Transformation
3) Definition of Bounded Transformation

Theorems proved in this video👇

1) A linear transformation T:N--N' is continuous on T iff it is continuous at a point (any) point of N.

2) A linear transformation T is continuous iff T is bounded.

3) A Linear transformation T:N--N' is Bounded (continuous) iff T maps bounded subset of N into bounded subset of N'

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Link to my other video lectures on Functional Analysis:

Lec 01👇(Normed Linear Space)

Lec 02 👇(Banach Space)

Lec 03 👇(Quotient Space)

Lec 04 👇(Examples of Normed Linear Space & Banach Space)

Lec 05 👇(Theorems on Normed Linear Space)

Lec 06 👇(Direct Sum in Normed Linear Space)

Lec 07 👇(Lp & L infinity Space)

Lec 08 👇(Proof of Holder's Inequality)

Lec 09 👇(Proof of Minkowski's Inequality)

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#ContinuousTransformations

[monikarawat]

let X=C(0, 1) with maximum morm we define K:X__X by Kf(x)= integration 0 to x f(x) dx then 1) k is continuous and bounded 2) norm of k
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