All Questions
7 questions
0
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1
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190
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Are the ideals in two $C^*$-algebras the same?
Let $V_{1}, V_{2}$ be the commuting isometries. By Wold decomposition theorem, we know that $V_{i}$ admits decomposition $$V_i \cong V^s_{i}\oplus V^{u}_{i},$$ where $V^{s}_{i}$ is the shift and $V^{u}...
- 139
5
votes
0
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137
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Trying to prove a seemingly easy fact on ideals of ternary C*-algebras
Currently I'm reading the paper by Abadie and Ferraro titled Applications of ternary rings to $C^*$-algebras.
Recall that a $C^{\ast}$-ternary ring is a complex Banach space $M$, equipped with a ...
- 1,115
2
votes
0
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305
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Ideals of maximal tensor product of $C^{\ast}$-algebras
Let $A$ and $B$ be $C^{\ast}$-algebras. It is well known that maximal tensor product of simple $C^{\ast}$-algebras need not be simple. So basically the ideal structure of $A\otimes_{max}B$ does not ...
- 1,115
3
votes
1
answer
146
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Modular and primitive ideals of $C_{0}(X,A)$
Let $A$ be $C^{\ast}$- Algebra and $X$ be a locally compact Hausdorff space and $C_{0}(X,A)$ be the set of all continuous functions from $X$ to $A$ vanishing at infinity. Define $f^{\ast}(t)={f(t)}^{\...
- 1,115
2
votes
2
answers
190
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Results which are known about ideals of spatial tensor product
I am studying about ideals of spatial (minimal) tensor product of $C^{\ast}$-algebras but I did not find any book/paper in which all the results are given.
What are some results or folklore which ...
- 1,115
0
votes
1
answer
236
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Need reference for ideals and representations of $C_0(X,A)$
Let $A$ be $C^{\ast}$- Algebra and $X$ be a locally compact Hausdorff space and $C_{0}(X,A)$ be the set of all continuous functions from $X$ to $A$ vanishing at infinity. Define $f^{\ast}(t)={f(t)}^{\...
- 1,115
2
votes
0
answers
99
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Invertibility modulo the intersection of ideals in $C^*$-algebras
This is a crosspost from math.se because it did not get any attention whatsoever. I therefore assume that it fits here better.
Let $\mathcal{A}$ be a $C^*$-algebra and $A \in \mathcal{A}$. I am ...
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