Related papers: Hyperinvariant subspaces for sets of polynomially …
We show that the non-zero multiples of the derivative operator and the non-zero multiples of non-trivial translation operators on the space of entire functions share a common hypercyclic subspace, i.e. a closed infinite-dimensional subspace…
We describe the proper closed invariant subspaces of the integration operator when it acts continuously on countable intersections and countable unions of weighted Banach spaces of holomorphic functions on the unit disc or the complex…
We characterize the semigroups of composition operators that are strongly continuous on the mixed norm spaces $H(p,q,\alpha)$. First, we study the separable spaces $H(p,q,\alpha)$ with $q<\infty,$ that behave as the Hardy and Bergman…
In this paper we study closed subspaces of ultradifferentiable functions which are invariant under the differentiation operator. We propose a version of spectral synthesis which takes into account the presence of non-trivial differentiation…
Real linear operators emerge in a range of mathematical physics applications. In this paper spectral questions of compact real linear operators are addressed. A Lomonosov-type invariant subspace theorem for antilinear compact operators is…
We address the existence of non-trivial closed invariant subspaces of operators $T$ on Banach spaces whenever their square $T^2$ have or, more generally, whether there exists a polynomial $p$ with $\mbox{deg}(p)\geq 2$ such that the lattice…
The famous Lomonosov's invariant subspace theorem states that if a continuous linear operator T on an infinite-dimensional normed space E "commutes" with a compact nonzero operator K, i.e., TK=KT, then T has a non-trivial closed invariant…
A contraction $T$ on a (complex, separable) Hilbert space is stable, or of class $C_{0\cdot}$, if $T^n\to 0$ in the strong operator topology. It is proved that for a non-stable pure subnormal contraction $T$ there exists a singular inner…
We show that a bounded quasinilpotent operator $T$ acting on an infinite dimensional Banach space has an invariant subspace if and only if there exists a rank one operator $F$ and a scalar $\alpha\in\mathbb{C}$, $\alpha\neq 0$, $\alpha\neq…
We introduce new polynomial invariants of a finite-dimensional semisimple and cosemisimple Hopf algebra A over a field by using the braiding structures of A. We investigate basic properties of the polynomial invariants including stability…
Finite rank perturbations of diagonalizable normal operators acting boundedly on infinite dimensional, separable, complex Hilbert spaces are considered from the standpoint of view of the existence of invariant subspaces. In particular, if…
We prove the existence of Hall polynomials for $x^2$-bounded invariant subspaces of nilpotent linear operators.
The main result of this paper is the existence of a hyperinvariant subspace of weighted composition operator $Tf=vf\circ\tau$ on $L^p([0,1]^d)$, ($1 \leq p \leq \infty$) when the weight $v$ is in the class of ``generalized polynomials'' and…
A particular case of [07] was generalized from contractions to polynomially bounded operators in [G19]. Namely, it is proved in [G19] that if the unitary asymptote of a polynomially bounded operator $T$ contains the bilateral shift of…
A closed subspace is invariant under the Ces\`aro operator $\mathcal{C}$ on the classical Hardy space $H^2(\mathbb D)$ if and only if its orthogonal complement is invariant under the $C_0$-semigroup of composition operators induced by the…
We present a general method for constructing operators without non-trivial invariant closed subsets on a large class of non-reflexive Banach spaces. In particular, our approach unifies and generalizes several constructions due to Read of…
We show that any bounded operator $T$ on a separable, reflexive, infinite-dimensional Banach space $X$ admits a rank one perturbation which has an invariant subspace of infinite dimension and codimension. In the non-reflexive spaces, we…
A particular case of results from [K2] is as follows. Let the unitary asymptote of a contraction $T$ contain the bilateral shift (of finite or infinite multiplicity). Then there exists an invariant subspace $\mathcal M$ of $T$ such that…
We prove the existence of the invariant subspaces of some operators in a real Banach space. For example, linear isometries have invariant subspaces
In this paper we study subspaces which are invariant under squares and cubes (separately as well as jointly) of unicellular backward weighted shift operators on a separable Hilbert space. The finite-dimensional subspaces are characterized…