Functional Analysis 18 | Compact Operators

Показать описание

Please consider to support me if this video was helpful such that I can continue to produce them :)

🙏 Thanks to all supporters! They are mentioned in the credits of the video :)

This is my video series about Functional Analysis where we start with metric spaces, talk about operators and spectral theory, and end with the famous Spectral Theorem. I hope that it will help everyone who wants to learn about it.

x

00:00 Introduction
02:39 Definition
03:13 Example

#FunctionalAnalysis
#VectorSpaces
#Mathematics
#LearnMath
#calculus

I hope that this helps students, pupils and others. Have fun!

(This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

Рекомендации по теме

Комментарии

9:02 By the way, it is not necessary for A to be bounded: it is suffisent to show A is point-wise bounded to apply Ascoli Theorem.

i.e. {g(x)/g in A} bounded for each x in [0, 1]

Jooolse

10 minutes with you >> 1 week in class

zachchairez

great video! the series is amazing 😊
at 9:20 I dont understand why bounded and equicontinuity holds for the closure as well?

jonasw

What software do you use to write the math? Also love your videos thanks for these!

kellyramsay

This might come in a later video, but what can we say about compact operators? Why would it be nice to know that an operator is compact?

aleksherstyuk

As usual, great ! Will there be anything about Hilbert-Schmidt operators ?

trondsaue

I'm couldn't really understand what happened at 3:53 for a particular f in C[0, 1], how and why are you defining Tf at s with another function k? What is the purpose of this k, and how did it come, in the first place?

AadityaVicramSaraf

can I ask for verification. if the operator is bounded, we can also say that image of B_1(0) of T also bounded?

ferry

How to show that the closure of an equicontinuous set of functions is equicontinuous though ?

StratosFair

8:40 uniformly -> uniformely -> uniformly 👀

Jooolse

Functional Analysis 18 | Compact Operators

Functional Analysis 18 | Compact Operators

Functional Analysis 16 | Compact Sets

Lecture 20: Compact Operators and the Spectrum of a Bounded Linear Operator on a Hilbert Space

Lecture 18: The Adjoint of a Bounded Linear Operator on a Hilbert Space

An Introduction to Compact Sets

Functional Analysis Review - Part 1 - Metric Spaces

The Fundamental Theorem of Functional Analysis

Functional Analysis 33 | Spectrum of Compact Operators

read this to learn functional analysis

Functional Analysis 34 | Spectral Theorem for Compact Operators [dark version]

This chapter closes now, for the next one to begin. 🥂✨.#iitbombay #convocation

Functional Analysis 3 | Open and Closed Sets

Functional analysis | Example of compact operator

Doctorate program: Functional Analysis - Lecture 36: An application to integral operators

Functional Analysis (MTH-FA) Lecture 18

Compact linear maps

How to eat Roti #SSB #SSB Preparation #Defence #Army #Best Defence Academy #OLQ

Functional Analysis 17 | Arzelà–Ascoli Theorem [dark version]

Lecture 1: Basic Banach Space Theory

Doctorate program: Functional Analysis - Lecture 14: Reflexive spaces

Spectrum of a Compact Operator (IFA21 Video 18)

How small are atoms?

Cosplay by b.tech final year at IIT Kharagpur

18 Functional Analysis | Bounded Set Beautiful Example | Bounded Set in Normed Linear Space