International Journal of Functional Analysis, Operator Theory and Applications
Volume 2, Issue 2, Pages 133 - 168
(December 2010)
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ON A LOCAL STRUCTURE IN RICKART ALGEBRAS - DEFINITIONS AND BASIC PROPERTIES
Dmitry Sh. Goldstein and Alexander A. Katz
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Abstract: We introduce and study locally weakly ![](/admin/Images/rcp58we_int19.gif)
-algebras (locally weakly Rickart ![](/admin/Images/rcp59we_int20.gif)
-algebras) and locally ![](/admin/Images/rcp58we_int19.gif)
-algebras (locally Rickart ![](/admin/Images/rcp59we_int20.gif)
-algebras) as a locally multiplicatively-convex generalization of weakly Rickart ![](/admin/Images/rcp59we_int20.gif)
-algebras and Rickart ![](/admin/Images/rcp60we_int21.gif)
-algebras, respectively. Among other basic properties of these algebras, it is established:
� That a locally -algebra is a locally -algebra iff there exists its Arens-Michael decomposition consisting entirely of -algebras;
� That a bounded part of a locally -algebra is a -algebra;
� The Spectral Theorem and The Polar Decomposition Theorem for �locally -algebras. |
Keywords and phrases: weakly Rickart ![](/admin/Images/rcp57weakly18.gif)
-algebras, Rickart ![](/admin/Images/rcp57weakly18.gif)
-algebras, locally weakly Rickart ![](/admin/Images/rcp57weakly18.gif)
-algebras, locally Rickart ![](/admin/Images/rcp57weakly18.gif)
-algebras, Hausdorff projective limit, ![](/admin/Images/rcp57weakly18.gif)
-algebras. |
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