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تسجيل مستخدم جديدTheory of $B(X)$-module -Algebraic module structure of generally-unbounded infinitesimal generators-
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تأليف
Yoritaka Iwata
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The concept of logarithmic representation of infinitesimal generators is introduced, and it is applied to clarify the algebraic structure of bounded and unbounded infinitesimal generators. In particular, by means of the logarithmic representation, the bounded components can be extracted from generally-unbounded infinitesimal generators. In conclusion the concept of module over a Banach algebra is proposed as the generalization of Banach algebra. As an application to mathematical physics, the rigorous formulation of rotation group, which consists of unbounded operators being written by differential operators, is provided using the module over a Banach algebra.
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