IDEAL J *-ALGEBRAS
A C *-algebra A is called an ideal C * -algebra (or equally a dual algebra) if it is an ideal in its bidual A**. M.C.F. Berglund proved that subalgebras and quotients of ideal C*-algebras are also ideal C*-algebras, that a commutative C *-algebra A is an ideal C *-algebra if and only if it is isomor...
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| Format: | Article |
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| Language: | English |
| Published: |
University of Tehran
1994-06-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
| Online Access: | https://jsciences.ut.ac.ir/article_31380_9d9445565a925df07e365566e8e4ea9d.pdf |
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| Summary: | A C *-algebra A is called an ideal C * -algebra (or equally a dual algebra) if it
is an ideal in its bidual A**. M.C.F. Berglund proved that subalgebras and
quotients of ideal C*-algebras are also ideal C*-algebras, that a commutative
C *-algebra A is an ideal C *-algebra if and only if it is isomorphicto C (Q) for
some discrete space ?. We investigate ideal J*-algebras and show that the
above results can be generalized to that of .I*-algebras. Furthermore, it is
proved that if A is an ideal ,J*-algebra, then sp(a* a) has no nonzero limit point
for each a in A and consequently A has semifinite rank and is a restricted
product of its simple ideals |
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| ISSN: | 1016-1104 2345-6914 |