All Questions
10 questions with no upvoted or accepted answers
9
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240
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What is known about when $vN(G)$ is a factor, for a locally compact group $G$?
When $G$ is a discrete group, it is an elementary result in the theory of von Neumann algebras that the group von Neumann algebra $vN(G)$ is a factor if and only if $G$ is an ICC group.
What is known ...
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4
votes
0
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114
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Coming up with a represenation for sum of functions in the Fourier algebra
This is my first overflow question, so let me apologize in advance if this belongs on http://math.stackexchange.com.
Let $G$ be a discrete group.
Let $\lambda:G\to B(\ell^{2}(G))$ be the left ...
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3
votes
0
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162
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The essential norm where some Fourier coefficients are fixed
Let us denote $C_{2\pi}$ by the set of all $2\pi$-periodic continuous functions $f:\mathbb{R}\to \mathbb{R}$.
Q. Let $\phi\in C_{2\pi}$. Is the following statement valid?
$$\|\phi\|_2=\inf_{g\in C_{2\...
- 4,058
3
votes
0
answers
211
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Arveson spectrum for a unitary representation of a group on a Hilbert space
Although this is not research, I think the question is a little bit too specific for math.stackexchange
Let $G = \mathbb{R}$. By Stone's theorem, $U(t)\in\mathcal{B}(\mathcal{H})$ is generated by a ...
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3
votes
0
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301
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What information about a locally compact group $G$ is encoded in $C_r^\ast(G)$ which is not in $L^1(G)$?
Let $G$ be a locally compact group and let $ C_r^\ast(G) $ denote its reduced group $C^\ast$-algebra. Many features of a $G$ can be realized from $L^1(G)$ or $C_r^\ast(G)$. For example, $G$ is ...
user23860
2
votes
0
answers
149
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A closed ideal in $L^1(T)$
Let $\mathbb{T}$ be the unit circle and consider the convolution group algebra $L^1(\mathbb{T})$. Let $I_n$ be the closed ideal generated by the polynomial $p_n(z)=z^n-1$ in $L^1(\mathbb{T})$.
Let $I=...
- 4,058
2
votes
0
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117
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Is the cone of positive elements in $L^1(G)$ norm closed?
Let's consider $L^1(G)$, the Banach $*$- algebra of all Lebesgue integrable functions on the locally compact group $G$. Put $L^1(G)_+$ by the cone of positive elements given by $\{\sum_1^n f_i^**f_i: ...
- 4,058
2
votes
0
answers
200
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Fredholmness and invertibility in a C* algebra generated convolution-type operators
Let $PC$ be the algebra of complex-valued, piecewise-continuous functions from $[-\infty,+\infty]$, $SO$ be the algebra of bounded, continuous, complex-valued functions on $\mathbb R$ which are slowly ...
- 21
1
vote
0
answers
79
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A problem arising from Wiener-Levy theorem on the real line
Theorem (Wiener-Levy). Let $A(\mathbb{T})$ be the Fourier-algebra on the unit circle $\mathbb{T}$. Let $f$ be in $A(\mathbb{T})$ and suppose that $F$ is an analytic function on the range of $f$. Then $...
- 4,058
0
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0
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85
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An amenable operator algebra has the total reduction property
This is from
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/CB20539885C03522D141C34024707702/S1446788700014026a.pdf/div-class-title-operator-algebras-with-a-reduction-property-...
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