Tagged Questions
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vote
1answer
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simply polar elements in a ring
An element $a$ in a ring $A$ with identity is said to be simply polar if there is $b$ for which $a=aba$, with $ab=ba$.
If in addition $b=bab$ then such an element $b$ is unique.
The question is ...
1
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1answer
34 views
Prime ideal for the Banach algebra
The maximal ideal and Jacobson radical often appear in the Banach algebra theory, but I do not see the prime and nilradical in it.
We can define a prime for a Banach algebra following the ring ...
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2answers
79 views
Commutativity in a Unital Banach Algebra
Let $ A $ be a unital Banach algebra and $ S $ a non-empty subset of $ A $. The centralizer of $ S $ is defined as
$$
Z(S) \stackrel{\text{def}}{=} \{ a \in A ~|~ \text{$ as = sa $ for all $ s \in S ...
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0answers
85 views
Banach modules; ambiguous terminology
In the following article, S. Grabiner very often writes "Banach module $A$ finitely dimensional over its radical". What does it mean? Does it mean that we think about the module as a module over its ...
