On the spectral theory of Rickart Ordered *-algebras

Alexander A. Katz; Dmitry Sh. Goldstein; Roman Sklyar

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On the spectral theory of Rickart Ordered *-algebras

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arxiv 1012.5262 v1 pith:QM4EPD64 submitted 2010-12-23 math.OA math.FA

Dmitry Sh. Goldstein , Alexander A. Katz , Roman Sklyar This is my paper · ORCID

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keywords algebrasspectralalgebraboundedcommutativeconsidereddefinedelement

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RO*-algebras are defined and studied. For RO*-algebra T, using properties of partial order, it is established that the set of bounded elements can be endowed with C*-norm. The structure of commutative subalgebras of T is considered and the Spectral Theorem for any self-adjoint element of T is proven.

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