Related papers: Invariant subspaces of Voiculescu's circular opera…
Let $R$ be the hyperfinite ${\rm II}_1$ factor and let $u,v$ be two generators of $R$ such that $u^*u=v^*v=1$ and $vu=e^{2\pi i\theta} uv$ for an irrational number $\theta$. In this paper we study the class of operators $uf(v)$, where $f$…
We construct a family of subalgebras of the Gerstenhaber algebra of differential operators. The subalgebras are labeled by subsets of the additive group ${\mathbb Z}^n$ that are closed under addition. Each subalgebra is invariant under the…
This paper is a sequel to [6]. In that paper we transferred the discussions in [1] and [13] concerning almost invariant half-spaces for operators on complex Banach spaces to the context of operators on Hilbert space, and we gave easier…
Voiculescu's notion of asymptotic free independence is known for a large class of random matrices including independent unitary invariant matrices. This notion is extended for independent random matrices invariant in law by conjugation by…
After introducing a natural notion of continuous fields of locally convex spaces, we establish a new theory of strongly continuous families of possibly unbounded self-adjoint operators over varying Hilbert spaces. This setting allows to…
A criterion to obtain frequent hypercyclicity for a sequence of convolution operators on the space of entire functions on the complex plane is provided. The criterion involves that the generating functions of the operators do not vanish on…
We consider the Toeplitz operators on the weighted Bergman spaces over the unit ball $\mathbb{B}^n$ and their analytic continuation. We proved the commutativity of the $C^*-$algebras generated by the analytic continuation of Toeplitz…
We establish a connection between compactness of Hankel operators and geometry of the underlying domain through compactness multipliers for the $\overline{\partial}$-Neumann operator. In particular, we prove that any compactness multiplier…
Let {a,b} and {c,d} be two pairs of bounding simple closed curves on an oriented surface which intersect nontrivialy. We prove that if these pairs are invariant under the action of an orientation reversing involution, then the corresponding…
A systematic exposition is given of the theory of invariant differential operators on a not necessarily reductive homogeneous space. This exposition is modelled on Helgason's treatment of the general reductive case and the special…
Cohomology spaces of the Poisson superalgebra realized on smooth Grassmann-valued functions with compact support on $R^{2n}$ ($C^{2n}) are investigated under suitable continuity restrictions on cochains. The first and second cohomology…
Complex Hadamard matrices are biunitaries for spin model commuting squares. The corresponding subfactor standard invariant can be identified with the $1$-eigenspace of the angle operator defined by Jones. We identify the angle operator as…
Let $\Free_n$ denote the free group with $n$ generators $g_1, g_2, ..., g_n$. Let $\lambda$ stand for the left regular representation of $\Free_n$ and let $\tau$ be the standard trace associated to $\lambda$. Given any positive integer $d$,…
For every operator space $X$ the $C^\ast$-algebra containing it in a universal way is residually finite-dimensional (that is, has a separating family of finite-dimensional representations). In particular, the free $C^\ast$-algebra on any…
Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three…
The theorem on the existence of maximal nonnegative invariant subspaces for a special class of dissipative operators in Hilbert space with indefinite inner product is proved in the paper. It is shown in addition that the spectra of the…
We prove that reiteratively hypercyclic operators have perfect spectrum. Consequently, it follows that there exist separable infinite dimensional Banach spaces that do not support any reiteratively hypercyclic operator. For this, we study…
In this paper we show that every bounded linear operator T on a Hilbert space H has a closed non-trivial invariant subspace.
We study geometric properties of varieties associated with invariant subspaces of nilpotent operators. There are reductive algebraic groups acting on these varieties. We give dimensions of orbits of these actions. Moreover, a combinatorial…
Voiculescu's random matrix model for freeness is extended to the non-Gaussian case and also the case of constant block diagonal matrices. Thus we are able to investigate free products of free group factors with matrix algebras and with the…