mathematics

Masamichi Takesaki

Masamichi Takesaki is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Masamichi Takesaki rather than just read about it. In short: Masamichi Takesaki (竹崎正道; born July 18, 1933, in Sendai) is a Japanese mathematician working in the theory of operator algebras. Takesaki studied at Tohoku University, earning a bachelor's degree in 1956, a master's degree in 1958 and a doctorate in 1965.

Key takeaways

Masamichi Takesaki belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Masamichi Takesaki to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Masamichi Takesaki from memory before moving on to harder problems.

Reference excerpt

Masamichi Takesaki (竹崎正道; born July 18, 1933, in Sendai) is a Japanese mathematician working in the theory of operator algebras. Takesaki studied at Tohoku University, earning a bachelor's degree in 1956, a master's degree in 1958 and a doctorate in 1965. Beginning in 1958 he was a research assistant at the Tokyo Institute of Technology and from 1965 to 1968 he was an associate professor at Tohoku University. From 1968 to 1969 he was a visiting associate professor at the University of Pennsylvania. In 1970, he became a professor at the University of California, Los Angeles. He was also a visiting professor at Aix-Marseille University (1973–74) and Bielefeld University (1975–76). He is known for the Tomita–Takesaki theory, which is about modular automorphisms of von Neumann algebras. This theory was initially developed by Minoru Tomita until 1967, but his work was published only partially (in Japanese) and was quite difficult to understand, drawing little notice, before being presented by Takesaki in 1970 in a book. In 1970, he was an invited speaker at the International Congress of Mathematicians in Nice; his talk was about one parameter automorphism groups and states of operator algebras. In 1990 he was awarded the Fujiwara Science Prize. He is a fellow of the American Mathematical Society.

Works Tomita's theory of modular Hilbert algebras and its applications, lecture notes mathematics, band 128, Springer Verlag 1970 Theory of operator algebras, 3 volumes, encyclopedia of mathematical sciences, Springer-Verlag, 2001–2003 (the first volume was published 1979 in 1. Edition)

Worked examples

Example 1 — a first encounter with Masamichi Takesaki

Start with the simplest possible case. Write down what Masamichi Takesaki claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Masamichi Takesaki before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Masamichi Takesaki ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Masamichi Takesaki

In research: Masamichi Takesaki appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Masamichi Takesaki in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Masamichi Takesaki is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1933 births, 20th-century Japanese mathematicians, 21st-century Japanese mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Masamichi Takesaki outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Masamichi Takesaki in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Masamichi Takesaki means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Masamichi Takesaki out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Masamichi Takesaki in simple terms?

Why does Masamichi Takesaki matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Masamichi Takesaki?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Masamichi Takesaki.