Researcher's Information

Professor

OSAKA, Hiroyuki

Mathematics

Operator Algebras and Operator Theory

Functional analysis which is the abstraction of mathematical models for use in revealing their essence is the main subject of this laboratory; however, recently, various graduate level research that includes mathematical physics, braid theory, topology, partial differential equations and probability theory are also taking place. We are also working on graduate level research linked to educational material for use in for junior high and high school education. 
Operator algebras, which is known as “an infinite dimensional linear algebra”, is the research subject. Banach space theory was introduced by Stefan Banach and developed as an extension of a function space on a compact metric space. In particular, we are working on the classification problem of C*- algebras generated by inserting an algebraic structure within them. 
Recently we have also been working on a problem connected to a monotonically increasing function that is applicable in economic theory and achieving a new result for Jensen’s inequality, which is a generalization of the arithmetic and geometric means that are presumably so familiar to high school students.
  • Both the arithmetic and geometric means can be derived using the above expression. Have a go at calculating them!!