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Abstract: In this paper we solve several problems concerning joint similarity ton-tuples of operators in noncommutative varieties in $B\cH^n 1$ associatedwith positive regular free holomorphic functions in $n$ noncommuting variablesand 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 thecorresponding variety can be seen as noncommutative multivariable analogues ofAgler-s $m$-hypercontractions.



Author: Gelu Popescu

Source: https://arxiv.org/







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