相关论文: A note on the spectrum of irreducible operators an…

We prove that any Iterated Function System of circle homeomorphisms with at least one of them having dense orbit, is asymptotically stable. The corresponding Perron-Frobenius operator is shown to satisfy the e-property, that is, for any…

Each bounded operator T on an infinite dimensional Hilbert space H is a sum of three operators that are similar to positive operators; two such operators are sufficient if T is not a compact perturbation of a scalar. The spectra of L\"uders…

We previously introduced the class of DT--operators, which are modeled by certain upper triangular random matrices, and showed that if the spectrum of a DT-operator is not reduced to a single point, then it has a nontrivial, closed,…

We consider the Schroedinger operator L_{\alpha} on the half-line with a periodic background potential and the Wigner-von Neumann potential of Coulomb type: csin(2\omega x+d)/(x+1). It is known that the continuous spectrum of the operator…

We study the spectrum of the linear operator $L = - \partial_{\theta} - \epsilon \partial_{\theta} (\sin \theta \partial_{\theta})$ subject to the periodic boundary conditions on $\theta \in [-\pi,\pi]$. We prove that the operator is closed…

The Invariant Subspace Problem (ISP) for Hilbert spaces asks if every bounded linear operator has a non-trivial closed invariant subspace. Due to the existence of universal operators (in the sense of Rota), the ISP may be solved by…

We define a class of pseudo-ergodic non-self-adjoint Schr\"odinger operators acting in spaces $l^2(X)$ and prove some general theorems about their spectral properties. We then apply these to study the spectrum of a non-self-adjoint Anderson…

We prove that the spectrum of a Schrodinger operator that is periodic in certain directions and super-exponentially decaying in the others is purely absolutely continuous.

We consider a normal operator $T$ on a Hilbert space $H$. Under various assumptions on the spectrum of $T$, we give bounds for the spectrum of $T+A$ where $A$ is $T$-bounded with relative bound less than 1 but we do not assume that $A$ is…

A bounded operator $u$ on $X$ is called rigid when there is an increasing sequence of positive integers $(n_k)_{k\geq 1}$, such that for every $x$ in $X$ we have $\lim_{k \rightarrow +\infty} u^{n_k} x = x$. For any $r$ in $[0,1]$, we…

We study the Schr\"odinger operator with a potential given by the sum of the potentials for harmonic oscillator and imaginary cubic oscillator and we focus on its pseudospectral properties. A summary of known results about the operator and…

In \cite{BAMU}, an ergodic theorem \`a la Birkhoff-von Neumann for the action of the fundamental group of a compact negatively curved manifold on the boundary of its universal cover is proved. A quick corollary is the irreducibility of the…

In this paper we study boundedness and detailed spectral properties for the Ces\`aro-Hardy operator and some generalizations in $L^p[0,1]$. The study employs $C_0$-semigroup theory, expressing the Ces\`aro-Hardy operators and their dual…

In this paper, we show that every pseudo B-Fredholm operator is a pseudo Fredholm operator. Afterwards, we prove that the pseudo B-Weyl spectrum is empty if and only if the pseudo B-Fredholm spectrum is empty. Also, we study a symmetric…

Let $H$ be an infinite dimensional separable Hilbert space, $B(H)$ the $C^*$-algebra of all bounded linear operators on $H,$ $U(B(H))$ the unitary group of $B(H)$ and ${\cal K}\subset B(H)$ the ideal of compact operators. Let $G$ be a…

In this paper we examine the asymptotic structure of the pseudospectrum of the singular Sturm-Liouville operator $L=\partial_x(f\partial_x)+\partial_x$ subject to periodic boundary conditions on a symmetric interval, where the coefficient…

Let $T$ be a rooted, countable infinite tree without terminal vertices. In the present paper, we characterize the spectra, self-adjointness and positivity of Toeplitz operators on the spaces of $p$-summable functions on $T$. Moreover, we…

We consider resonances for fourth order differential operators on the half-line with compactly supported coefficients. We determine asymptotics of a counting function of resonances in complex discs at large radius, describe the forbidden…

We consider discrete one-dimensional Schr\"odinger operators with strictly ergodic, aperiodic potentials taking finitely many values. The well-known tendency of these operators to have purely singular continuous spectrum of zero Lebesgue…

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…