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Sep 28 |
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Grothendieck on Topological Vector Spaces
I forgot the category of convenient spaces: ncatlab.org/nlab/show/convenient+vector+space. It seems to me it possesses some of these properties (without auto-duality, as far as I know). @PeterMichor can clarify this. |

Sep 28 |
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Grothendieck on Topological Vector Spaces
As to $\ell_1$, this is a question of habits. What we see every day becomes our own, like our relatives or friends. |

Sep 28 |
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Grothendieck on Topological Vector Spaces
Yemon, no, it isn't. Because this duality generates a closed monoidal category ${\tt Ste}$ of stereotype spaces, the second one in Analysis after the category ${\tt Ban}$ of Banach spaces with this property, and this auto-duality (with many other remarkable properties) makes ${\tt Ste}$ better than ${\tt Ban}$. IMHO. :) |

Sep 28 |
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Grothendieck on Topological Vector Spaces
As an illustration: who knows that every Banach space $X$ becomes relexive, $X^{\star\star}=X$, if we endow its dual space $X^\star$ with the compact-open topology? This was found in 1952 by Marianne Smith. When I am telling this to people they are surprised. Formally this is absurd: the simple explanation is less known than the intricate one. A reference for those who find this unexpected: en.wikipedia.org/wiki/Stereotype_space. |

Sep 28 |
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Grothendieck on Topological Vector Spaces
I upvoted Yemon's comment, but this was a mistake. In my opinion, the theory of TVS is indeed dead, and the most part of the guilt for this lies on Alexander Grothedieck. It must have been evident from the very beginning that there is something wrong in this abundance of topologies on the dual space, duality theories, counter-examples, etc. After its birth the theory immediately turned into a long list of counterexamples. The scientific explanation can't be so intricate, knotty, this is an abuse of professional knowledge. |

Sep 28 |
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Tangent space of the Fourier algebra $A(G)$
Thank you, Yemon! |

Sep 27 |
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Tangent space of the Fourier algebra $A(G)$
I thought, when $G$ is not discrete there must be at least usual derivatives $\frac{\partial}{\partial x_i}$... They are not continuous here? |

Sep 27 |
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Tangent space of the Fourier algebra $A(G)$
Yemon, how can this be? There are non-smooth functions in $A(G)$? |

Sep 25 |
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A generalization of real characters on a group
Neil, but I suppose you mean $A[t]/\{t^{n+1}\}$, the quotient algebra. |

Sep 24 |
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A generalization of real characters on a group
@NeilStrickland, yes, excuse me for the mistake in the second condition! I corrected this. |

Sep 24 |
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A generalization of real characters on a group
@YCor, yes initially $G$ and $A$ both were algebras. I reformulated this for the case when $G$ is a group. |

Sep 24 |
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When is the Fourier algebra $A(G)$ enough close to the Fourier-Stieltjes algebra $B(G)$?
Yemon, I think you meant $A(G)\subseteq C_0(G)$. |

Sep 24 |
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When is the Fourier algebra $A(G)$ enough close to the Fourier-Stieltjes algebra $B(G)$?
Ah, I see! No, I meant the usual set of zeroes: $\text{Ker}f=\{x:\ f(x)=0\}$. Yemon, where is this written, about "iff $G$ is amenable"? |

Sep 24 |
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When is the Fourier algebra $A(G)$ enough close to the Fourier-Stieltjes algebra $B(G)$?
Yemon, thank you, yes, I mean the usual kernel. Actually, I don't know, in which other sense it can be understood. Can you give a reference? |

Sep 19 |
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When is the induced representation factored through the initial one?
My $H$ is normal. Ben, I need a reference. I must refer to a textbook or to a paper in my text. |

Sep 18 |
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When is the induced representation factored through the initial one?
Ben, can this be true when $H$ is normal? |

Sep 16 |
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When is the induced representation factored through the initial one?
Thank you, Ben. |

Sep 15 |
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When is the induced representation factored through the initial one?
I tried to input a diagram, but they seem to do not work here. Is it possible to use diagrams in MO? |

Aug 17 |
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Identities that connect antipode with multiplication and comultiplication
This is what I need, thank you! |

Aug 13 |
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Is the ideal of functions vanishing at a set complementable in $C(X)$?
@NarutakaOZAWA, could you, please, give the reference? |