Related papers: Invariant Subspaces of Nilpotent Linear Operators.…

The aim of this work is to study the structure of bounded finite potent endomorphisms on Hilbert spaces. In particular, for these operators, an answer to the Invariant Subspace Problem is given and the main properties of its adjoint…

Given two nilpotent endomorphisms, we determine when their lattices of hyperinvariant subspaces are isomorphic. The study of the lattice of hyperinvariant subspaces can be reduced to the nilpotent case when the endomorphism has a…

In this paper, we study {\it operator spaces\/} in the sense of the theory developed recently by Blecher-Paulsen [BP] and Effros-Ruan [ER1]. By an operator space, we mean a closed subspace $E\subset B(H)$, with $H$ Hilbert. We will be…

Let ${\mathfrak g}$ be a finite dimensional Lie algebra over a field of characteristic 0, with solvable radical ${\mathfrak r}$ and nilpotent radical ${\mathfrak n}=[{\mathfrak g},{\mathfrak r}]$. Given a finite dimensional ${\mathfrak…

Let $G$ be a linear algebraic group over a field $k$, and let $V$ be a $G$-module. Recall that the nullcone of $(G,V)$ is the set of points $v$ in $V$ with the property that $f(v)=0$ for every positive degree homogeneous invariant $f$ in…

In 1960's I. Gelfand posed a problem: describe indecomposable representations of any simple infinite dimensional Lie algebra of polynomial vector fields. Here, by applying the elementary technique of Gelfand and Ponomarev, a toy model of…

In theory and practice of inverse problems, linear operator equations $Tx=y$ with compact linear forward operators $T$ having a non-closed range $\mathcal{R}(T)$ and mapping between infinite dimensional Hilbert spaces plays some prominent…

Let $L= -\Delta+ V$ be a Schr\"odinger operator on $\mathbb R^d$, $d\geq 3$, where $V$ is a nonnegative potential, $V\ne 0$, and belongs to the reverse H\"older class $RH_{d/2}$. In this paper, we study the commutators $[b,T]$ for $T$ in a…

A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis (the generalized Bochner problem) is given. The main result is that any operator with…

We consider several vertex operator (super)algebras closely related to $V_{-1}(\frak{sl} (n) )$, $n \ge 3$ : (a) the parafermionic subalgebra $K(\frak{sl}(n),-1)$ for which we completely describe its inner structure, (b) the vacuum algebra…

We prove the existence of the invariant subspaces of some operators in a real Banach space. For example, linear isometries have invariant subspaces

The goal of this paper is to generalize the theory of triangularizing matrices to linear transformations of an arbitrary vector space, without placing any restrictions on the dimension of the space or on the base field. We define a…

Four possible definitions of the commutation relation $[S,T]=\Id$ of two closable unbounded operators $S,T$ are compared. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space $\H$ where 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 introduce a traceable operator-algebraic framework for incompressible transport on M= T3 (and, more generally, compact Riemannian manifolds endowed with a smooth invariant probability measure). Given an autonomous divergence-free…

In this paper, we first prove that $u,v,h$ are linearly dependent over ${\bf K}$ if $JH$ is nilpotent and $H$ has the form: $H=(u(x,y,z),v(u,h),h(x,y))$ with $H(0)=0$ or $H=(u(x,y),v(u,h),h(x,y,z))$ with $H(0)=0$. Then we classify…

Let $V$ be a vector space and $U$ a fixed subspace of $V$. We denote the semigroup of all linear transformations on $V$ under composition of functions by $L(V)$. In this paper, we study the semigroup of all linear transformations on $V$…

This paper is a follow-up contribution to our work [20] where we discussed some invariant subspace results for contractions on Hilbert spaces. Here we extend the results of [20] to the context of n-tuples of bounded linear operators on…

In this work we study Schatten-von Neumann classes of tensor products of invariant operators on Hilbert spaces. In the first part we first deduce some spectral properties for tensors of anharmonic oscillators thanks to the knowledge on…

The normal form for an n-dimensional map with irreducible nilpotent linear part is determined using sl2-representation theory. We sketch by example how the reducible case can also be treated in an algorithmic manner. The construction (and…