Tosio Kato | Biography

Tosio Kato, whose career in mathematics ranged over more than 40 years, made major contributions to the field of mathematical physics. A prolific writer, he produced hundreds of published articles during his career. His most important research, on perturbation theory, won him acclaim and awards in both his native country of Japan and in the United States, where he spent most of his career.

Kato was born on August 25, 1917, in Tochigiken, Japan, the son of Shoji and Shin (Sakamoto) Kato. He attended the University of Tokyo, where he received a bachelor's degree in 1941; he would receive a doctor of science degree from the university ten years later. In 1943, he began teaching at the University of Tokyo, and due to the stability this position provided he was able to marry Mizue Suzuki the following year.

Even before his appointment to full professorship at the university, which he achieved upon receiving his doctorate in 1951, Kato had begun to publish the beginnings of his research in perturbation theory. Perturbation theory is the study of a system which deviates slightly from a less complex, ideal system. This is an important field of research because most systems that mathematicians and physicists study are not ideal. Kato examined only the perturbation theory which relates to linear operators (functions). The groundbreaking work in the field had been accomplished by John Rayleigh and Erwin Schrödinger in the 1920s.

Kato's contributions to perturbation theorywere threefold. First, he laid the mathematical foundation for the theory, applying ideas in modern analysis and function theory. Second, he established the selfadjointness of Schrödinger operators--in other words, he showed that Schrödinger operators are symmetric. This was significant because these operators are a fundamental tool of quantum physics and knowledge of their symmetry makes their manipulation much simpler. Finally, he began the study of the spectral properties of the operators, which describes the variety of simple effects which the operators can have when applied to specific elements of a given set. This is important as it allows the operators to be described in terms of many simple effects which can be combined into larger ones. The term spectral is related to the way in which a complicated operator splits into distinct effects, as light can be split into distinct colors.

The culmination of his work was his definitive book on the subject, Perturbation Theory for Linear Operators, which he began writing in Japan and completed in the United States, after accepting a professorship at the University of California at Berkeley in 1962. Although the book did not appear until 1966, his home country had already recognized him as a leading researcher in his field, presenting him with the Asahi Award in 1960.

In the United States, Kato continued his research into perturbation theory and used functional analysis to solve problems in hydrodynamics and evolution equations. Even though Kato was well known in the American mathematical community by his hundreds of published articles, acknowledgement of the importance of his work came late in the United States. It was not until 1980 that the American Mathematical Society and the Society for Industrial and Applied Mathematics jointly awarded him the Norbert Wiener Prize for applied mathematics. In Japan, Kato continued to receive recognition. On the occasion of his retirement from the University of California in 1989, the University of Tokyo held a conference in his honor. The conference, entitled "The International Conference on Functional Analysis in Honor of Professor Tosio Kato," paid homage to Kato's many contributions in the field of mathematical physics. Kato died on October 2, 1999, of a heart attack in Oakland, California, at the age of 82.