Totally multiplicatively prime algebras
2002 ◽
Vol 132
(5)
◽
pp. 1145-1162
We introduce the totally multiplicatively prime algebras as those normed algebras for which there exists a positive number K such that K‖F‖‖a‖ ≤ ‖WF,a‖ for all F in M(A) (the multiplication algebra of A) and a in A, where WF,a denotes the operator from M(A) into A defined by WF,a(T) = FT(a) for all T in M(A). These algebras are totally prime and their multiplication algebra is ultraprime. We get the stability of the class of totally multiplicatively prime algebras by taking central closure. We prove that prime H*-algebras are totally multiplicatively prime and that the ℓ1-norm is the only classical norm on the free non-associative algebras for which these are totally multiplicatively prime.
2002 ◽
Vol 132
(5)
◽
pp. 1145-1162
◽
2013 ◽
Vol 12
(07)
◽
pp. 1350023
1999 ◽
Vol 27
(12)
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pp. 5723-5736
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1982 ◽
Vol 99
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pp. 605-613
Keyword(s):
1999 ◽
Vol 173
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pp. 309-314
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1970 ◽
Vol 28
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pp. 444-445
1973 ◽
Vol 31
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pp. 486-487
1970 ◽
Vol 28
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pp. 150-151
Keyword(s):
1976 ◽
Vol 34
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pp. 630-631