# Some quasinilpotent generators of the hyperfinite $mathrm{II} 1$ factor - Mathematics > Operator Algebras

Some quasinilpotent generators of the hyperfinite $mathrm{II} 1$ factor - Mathematics > Operator Algebras - Download this document for free, or read online. Document in PDF available to download.

Abstract: For each sequence $\{c n\} n$ in $l {1}\N$ we define an operator $A$ in thehyperfinite $\mathrm{II} 1$-factor $\mathcal{R}$. We prove that these operatorsare quasinilpotent and they generate the whole hyperfinite$\mathrm{II} 1$-factor. We show that they have non-trivial, closed, invariantsubspaces affiliated to the von Neumann algebra and we provide enough evidenceto suggest that these operators are interesting for the hyperinvariant subspaceproblem. We also present some of their properties. In particular, we show thatthe real and imaginary part of $A$ are equally distributed, and we find acombinatorial formula as well as an analytical way to compute their moments. Wepresent a combinatorial way of computing the moments of $A^{*}A$.

Author: ** Gabriel H. Tucci**

Source: https://arxiv.org/