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Last modified date：2009.10.13
Hideki KOSAKI
Professor
Graduate School
Undergraduate School
Academic Degree
Ph D
Field of Specialization
Functional Analysis
Outline Activities
I have been working on functional analysis, mainly the following three
subjects:
(i) Non-commutative Integration and Analysis on von Neumann Algebras
A von Neumann algebra together with a functional on it can be thought of
as a (non-commutative) measure space. I have been working on non-commutative
integration theory in this setting and various related analysis.
(ii) Index Theory for Type $III$ Factors
The index theory for operator algebras deals mainly with $II_1$ factors.
Type III factors sitting at the extreme opposite in the theory is equally
important. I worked on index theory for type $III$ factors and various
related subfactor analysis.
(iii) Study on Operator Inequalities
The essential difficulty of dealing with operators is non-commutativity,
and various notions of orders among them are needed to different purposes.
I have been working on miscellaneous inequalitites for operators and/or
related quantities.
For graduate courses, indivisual studies and lectures at other institutions
I choose appropriate topics from the above three, and explain various aspects
of the chosen ones.
Research
Educational
Educational Activities
Every year I teach freshman/sophomore classes (on either linear algebra or
calculus) . At the department of mathematics （or engineering school）
I offer various courses on analysis and functional analysis. In the last
five years I have taught the following subjects: general topology, Lebesgue
integral, complex functions, functional analysis, basic operator theory.
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