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Discrete spectra of
Author(s):
Masaharu
Kusuda
Abstract | References | Similar articles | Additional information
Abstract:
Let
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Masaharu
Kusuda
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-algebras and orthogonally closed submodules in Hilbert 
-modules
and 
be 
-algebras and let 
be an 
-
-imprimitivity bimodule. Then it is shown that if the spectrum 
of 
(resp. 
of 
) is discrete, then every closed 
-
-submodule of 
is orthogonally closed in 
, and conversely that if 
(resp. 
) is a 
-space and if every closed 
-
-submodule of 
is orthogonally closed in 
, then 
(resp. 
) is discrete. 
-algebras, North Holland, New York, 1982. 
-algebras and dual 
-algebras, Proc. Royal Soc. Edinburgh 131A (2001), 701-707. 
-algebras and complemented submodules in Hilbert 
-modules, Proc. Amer. Math. Soc. 131 (2003), 3075-3081. 
-modules, London Math. Soc. Lecture Note Series Vol. 210, Cambridge Univ. Press, Cambridge, 1994. 
-modules in which all closed submodules are complemented, Proc. Amer. Math. Soc. 125 (1997), 849-852. 
-algebras, Math. Surveys Monographs Vol. 60, Amer. Math. Soc., Providence, 1998. 
-modules in which all closed submodules are orthogonally closed, Proc. Amer. Math. Soc. 127 (1999), 2123-2125.