


到達目標 Target to be Reached

This lecture is on Hilbert space H and bounded linear operators on H. Purpose of this lecture is that students understand properties of Hilbert space H and theory of bounded linear operators on H. Moreover, this lecture is to be a basis of his research.


授業内容 Course Content

Hilbert space is a complete space with inner product. Hilbert space has many applications. Firstly I have a talk on basic properties of inner product and Hilbert space. Secondary I have a talk on basic properties of linear operators and spectral properties of linear operators.


授業計画 Course Planning

Schedule of the lecture:
1．About this lecture
2．Metric spaces
3．Normed spaces
4．Inner product
5．Hilbert space
6．Riesz representation theorem
7．Linear operators on a Hilbert space
8．Norm of a linear operator
9．Basic properties of operator norm
10．Spectrum of an operator
11．Spectral radius of an operator
12．Several class of operators
13．Operators and their spectra
14．Hyponormal operators
15．Summary of this lecture


授業運営 Course Management

Lectures are the basis for how teachers give their lessons. And sometimes teacher does quiz questions in a lecture.


評価方法 Evaluation Method

The final test is 90% and 10% is quiz questions.


オフィスアワー Office Hour (s)

From 12:30 to 13:00 on Monday and Tuesday.





