Joint similarity to operators in noncommutative varieties

Details Joint similarity to operators in noncommutative varieties Joint similarity to operators in noncommutative varieties

2010-04-12

arxiv.org/abs/1004.2021v2

Proc.London Math.Soc.(3)103(2011) 331-370

Mathematics

Functional Analysis

35 pages, corrected typos

Scientific paper

In this paper we solve several problems concerning joint similarity to n-tuples of operators in noncommutative varieties in $[B(\cH)^n]_1$ associated with positive regular free holomorphic functions in $n$ noncommuting variables and with sets of noncommutative polynomials in $n$ indeterminates, where $B(\cH)$ is the algebra of all bounded linear operators on a Hilbert space $\cH$. In particular, if $f=X_1+...+X_n$ and $\cP=\{0\}$, the elements of the corresponding variety can be seen as noncommutative multivariable analogues of Agler's $m$-hypercontractions.

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