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Results tagged with banach-algebras
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user 85784
1
vote
1
answer
132
views
The image of a derivation on a Banach algebra is contained in the kernel of a character
It is known that if $D$ is a continuous derivation on a commutative Banach algebra $\mathcal{A}$, then for any nonzero character $\theta$ on $\mathcal{A}$ we have $D(\mathcal{A})⊆ker\theta $. …
- 167
0
votes
1
answer
275
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The definiton of a multiplier on a Banach algebra
Let $A$ be a Banach algebra. Some textbooks define a (left ) multiplier as a map $T:A\rightarrow A$ satisfying $T(ab)=T(a)b$ for all $a,b\in A$ and assume that $A$ needs to be a without order Banach a …
- 167
1
vote
0
answers
128
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Decomposition of Banach bimodules of Banach algebras
Let $A$ and $B$ be Banach algebras, $\theta:A\rightarrow \mathbb{C}$ be a character (i.e., a multiplicative linear functional) and $A\oplus _{\theta} B$ be the $l^1$-direct sum of $A$ and $B$ equipped …
- 167
1
vote
0
answers
88
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An example of a Banach algebra with a specified property
I asked this question
(https://math.stackexchange.com/questions/3076735/an-example-of-a-banach-algebra-satisfying-given-conditions)
but unfortunately no one answered it. Please help me to find an exa …
- 167
2
votes
1
answer
140
views
Continuity of the derivations from semisimple Banach algebras
Let $A$ be a Banach algebra and $X$ a Banach $A$-bimodule. It is known that if $A$ is a $C^*$-algebra, then by Ringrose theorem every derivation $D:A\rightarrow X$ is continuous. Also, a famous theor …
- 167
0
votes
1
answer
250
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Banach algebra $A$ without an approximate identity but $A^2=A$
Please help me with the following question.
What are some examples of Banach algebra $A$ satisfying the following two conditions?
$1$.$ A $ does not have an approximate identity.
$2$. $A^2=A$. T …
- 167