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A Note on the Connectedness Problem for Nest Algebras
It has been conjectured that a certain operator $T$ belonging to the group $\mathcal {G}$ of invertible elements of the algebra $\operatorname {Alg} {\mathbf {Z}}$ of doubly infinite upper-triangular bounded matrices lies outside the connected component of the identity in $\mathcal {G}$. In this note we show that $T$ actually …