Operator algebra as an application of logarithmic representation of infinitesimal generators

Abstract

The operator algebra is introduced based on the framework of logarithmic representation of infinitesimal generators. In conclusion a set of generally-unbounded infinitesimal generators is characterized as a module over the Banach algebra.

To be published in J. Phys. Conf. Ser. (the proceedings of ISQS25)

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• Unbounded generalization of logarithmic representation of infinitesimal generators
• Theory of $B(X)$-module -Algebraic module structure of generally-unbounded infinitesimal generators-
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• Operator topology for logarithmic infinitesimal generators
• Recurrence formula for some higher order evolution equations