Operator algebras and noncommutative analysis

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Operators on a Hilbert space, a generalization of the Euclid space, play fundamental roles in analysis and quantum physics. The set of bounded operators B(H) on a Hilbert space H is closed under linear operations, product, and conjugation, and it is a typical example of an operator algebra. In this research, I performed structure analysis of operator algebras. In particular, I studied the structure of a 1-parameter semigroup of endomorphisms of B(H), and obtained new classification invariants and construction of new examples.