Invariant subspaces of the quasinilpotent DT-operator

DOI10.1016/S0022-1236(03)00167-8zbMath1087.47006arXivmath/0301112OpenAlexW1974862046MaRDI QIDQ1876254

Uffe Haagerup, Kenneth J. Dykema

Publication date: 16 August 2004

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0301112

zbMATH Keywords

von Neumann algebrainvariant subspacequasinilpotent operator

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) Invariant subspaces of linear operators (47A15)

Related Items (18)

On single commutators in II$_{1}$–factors ⋮ The non-microstates free entropy dimension of DT-operators ⋮ THE FREE ENTROPY DIMENSION OF SOME L^∞[0,1-CIRCULAR OPERATORS] ⋮ Matricial circular systems and random matrices ⋮ SPECTRAL PROPERTIES OF RANDOM TRIANGULAR MATRICES ⋮ MOMENT FORMULAS FOR THE QUASI-NILPOTENT DT-OPERATOR ⋮ Eigenvalues of non-Hermitian random matrices and Brown measure of non-normal operators: Hermitian reduction and linearization method ⋮ Berry-Esseen bounds for the multivariate ℬ-free CLT and operator-valued matrices ⋮ The Brown measure of a sum of two free random variables, one of which is triangular elliptic ⋮ Numerical Ranges in II₁ Factors ⋮ Some quasinilpotent generators of the hyperfinite \(\mathrm{II}_{1}\)-factor ⋮ On transitive algebras containing a standard finite von Neumann subalgebra ⋮ Limit theorems for free Lévy processes ⋮ Macroscale behavior of random lower triangular matrices ⋮ Power set and invariant subspaces of cyclic quasinilpotent operators ⋮ Invariant subspaces for operators in a general \(\text{II}_{1}\)-factor ⋮ Hyperinvariant subspaces for some \(B\)-circular operators ⋮ On powers of Stieltjes moment sequences, I

Cites Work

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• Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\)
• On the Lambert \(w\) function
• Multinomial identities arising from free probability theory.
• Combinatorial theory of the free product with amalgamation and operator-valued free probability theory
• DT-operators and decomposability of Voiculescu's circular operator
• Invariant subspaces of Voiculescu's circular operator

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