Related papers: Simultaneous upper triangular forms for commuting …

Results of Haagerup and Schultz (2009) about existence of invariant subspaces that decompose the Brown measure are extended to a large class of unbounded operators affiliated to a tracial von Neumann algebra. These subspaces are used to…

Using the spectral subspaces obtained in [HS], Brown's results on the Brown measure of an operator in a type II_1 factor (M,tr) are generalized to finite sets of commuting operators in M. It is shown that whenever T_1,..., T_n in M are…

The decompositions of an element of a finite von Neumann algebra into the sum of a normal operator plus an s.o.t.-quasinilpotent operator, obtained using the Haagerup--Schultz hyperinvariant projections, behave well with respect to…

We consider the Aluthge transform $|T|^{1/2}U|T|^{1/2}$ of a Hilbert space operator $T$, where $T=U|T|$ is the polar decomposition of $T$. We prove that the map that sends $T$ to its Aluthge transform is continuous with respect to the norm…

Joint spectra of tuples of operators are subsets in complex projective space. The corresponding tuple of operators can be viewed as an infinite dimensional analog of a determinantal representation of the joint spectrum. We investigate the…

We study Schur-type upper triangular forms for elements, T, of von Neumann algebras equipped with faithful, normal, tracial states. These were introduced in a paper of Dykema, Sukochev and Zanin; they are based on Haagerup-Schultz…

We prove a variety of results describing the possible diagonals of tuples of commuting hermitian operators in type $II_1$ factors. These results are generalisations of the classical Schur-Horn theorem to the infinite dimensional,…

Given a DT-operator $Z$ whose Brown measure is radially symmetric and has a certain concentration property, it is shown that $Z$ is not spectral in the sense of Dunford. This is accomplished by showing that the angles between certain…

The theory of direct integral decompositions of both bounded and unbounded operators is further developed; in particular, results about spectral projections, functional calculus and affiliation to von Neumann algebras are proved. For…

We show that every multivariable contractive weighted shift dilates to a tuple of commuting unitaries, and hence satisfies von Neumann's inequality. This answers a question of Lubin and Shields. We also exhibit a closely related $3$-tuple…

We investigate determinants of Koszul complexes of holomorphic functions of a commuting tuple of bounded operators acting on a Hilbert space. Our main result shows that the analytic joint torsion, which compares two such determinants, can…

Let $\mathbf{T} \equiv (T_1,\cdots,T_n)$ be a commuting $n$-tuple of operators on a Hilbert space $\mathcal{H}$, and let $T_i \equiv V_i P \; (1 \le i \le n)$ be its canonical joint polar decomposition (i.e.,…

For a countably decomposable finite von Neumann algebra $\mathscr{R}$, we show that any choice of a faithful normal tracial state on $\mathscr{R}$ engenders the same measure topology on $\mathscr{R}$ in the sense of Nelson (J. Func. Anal.,…

For three standard models of commutative algebras generated by Toeplitz operators in the weighted analytic Bergman space on the unit disk, we find their representations as the algebras of bounded functions of certain unbounded self-adjoint…

This paper mainly concerns the von Neumann algebras induced by a tuple of multiplication operators on Bergman spaces which arise essentially from holomorphic proper maps over higher dimensional domains. We study the structures and abelian…

Results about angles between Haagerup--Schultz projections for DT-operators whose measures have atoms are proved, which in some cases imply that such operators are non-spectral. Several examples are considered.

We introduce a notion called `maximal commuting piece' for tuples of Hilbert space operators. Given a commuting tuple of operators forming a row contraction there are two commonly used dilations in multivariable operator theory. Firstly…

We study Toeplitz operators with respect to a commuting $n$-tuple of bounded operators which satisfies some additional conditions coming from complex geometry. Then we consider a particular such tuple on a function space. The algebra of…

Motivated by Ball, Li, Timotin and Trent's Schur-Agler class version of commutant lifting theorem, we introduce a class, denoted by $\mathcal{P}_n(\mathcal{H})$, of $n$-tuples of commuting contractions on a Hilbert space $\mathcal{H}$. We…

A weighted sums of squares decomposition of positive Borel measurable functions on a bounded Borel subset of the Euclidean space is obtained via duality from the spectral theorem for tuples of commuting self-adjoint operators. The analogous…