Spectral theory of linear operators
35 videos • 49,765 views • by Nani's MathsClass
In this course, we shall be studying the spectral theory of linear operators. Course Instructor: Meenal Singhal
1
#1: Introduction
Nani's MathsClass
Download
2
#2: Learning about linear operators
Nani's MathsClass
Download
3
#3: Review of eigenvalues of matrices
Nani's MathsClass
Download
4
#4: Properties of eigenvalues and eigenvectors
Nani's MathsClass
Download
5
#5: Transition from linear algebra to operator theory
Nani's MathsClass
Download
6
#6: Spectral theory of normed spaces: Basic Concepts - I
Nani's MathsClass
Download
7
#7: Spectral theory of normed spaces: Basic Concepts - II
Nani's MathsClass
Download
8
#8: Spectral properties of bounded linear operators-I
Nani's MathsClass
Download
9
#9: Spectral properties of bounded linear operators-II
Nani's MathsClass
Download
10
#10: Spectral properties of bounded linear operators-III
Nani's MathsClass
Download
11
#11: Resolvent equation and commutativity
Nani's MathsClass
Download
12
#12: Motivation for spectral mapping theorem
Nani's MathsClass
Download
13
#13: Spectral mapping theorem
Nani's MathsClass
Download
14
#14: Linear independence of eigenvectors of a linear operator
Nani's MathsClass
Download
15
#15: Role of complex analysis in spectral theory
Nani's MathsClass
Download
16
#16: The spectrum of a bounded linear operator is non-empty
Nani's MathsClass
Download
17
#17: Result on spectral radius
Nani's MathsClass
Download
18
#18: What is normed and Banach algebra?
Nani's MathsClass
Download
19
#19: Connection of spectra with Banach algebra
Nani's MathsClass
Download
20
#20: Properties of Banach algebra-I
Nani's MathsClass
Download
21
#21: Properties of Banach algebra-II
Nani's MathsClass
Download
22
#22: Properties of Banach algebra-III
Nani's MathsClass
Download
23
#23: Resolvent equation in Banach algebra
Nani's MathsClass
Download
24
#24: What are compact linear operators?
Nani's MathsClass
Download
25
#25: The compactness criterion
Nani's MathsClass
Download
26
#26: When does the limit of a sequence of compact linear operators be compact?
Nani's MathsClass
Download
27
#27: Property of compact linear operators to convert weakly into strongly convergent sequences
Nani's MathsClass
Download
28
#28: What is total boundedness?
Nani's MathsClass
Download
29
#29: Result on total boundedness
Nani's MathsClass
Download
30
#30: Total boundedness implies boundedness
Nani's MathsClass
Download
31
#31: Separability of range of compact linear operator
Nani's MathsClass
Download
32
#32: Compact linear extension of compact operator
Nani's MathsClass
Download
33
#33: What is the adjoint operator?
Nani's MathsClass
Download
34
#34: Compactness of an adjoint operator
Nani's MathsClass
Download
35
#35: Spectral properties of compact linear operator
Nani's MathsClass
Download