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7 votes

Linear map between projective finitely generated Hilbert modules is adjointable

There is a difference between algebraically finitely generated and topological finitely generated Hilbert $C^*$-modules. Consider $C_0((0,1])$ - the $C^*$-algebra of all continuous functions on the ...
Michael Frank's user avatar
4 votes

Rescaling Fourier coefficients of a continuous function by a bounded sequence

$a_n=\operatorname{sign}(n)$ is a bounded sequence that is not a multiplier on $C(S)$. The corresponding operator $L^2(S)\to L^2(S)$ is the Hilbert transform $$ (Hf)(x) = \lim_{h\to 0+} \int_{|y-x|>...
Christian Remling's user avatar
8 votes

type II$_1$ subalgebra of type III$_1$ factor

Such a relative commutant $N' \cap M$ can even be any factor. Choose any type III$_1$ factor $P$ with a type II$_1$ subfactor $N \subset P$ with trivial relative commutant $N' \cap P = \mathbb{C} 1$. ...
Stefaan Vaes's user avatar
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