相关论文: Note on Near Subnormal Weighted Shifts
In this paper we initiate the study of a fundamental yet untapped random model of non-selfadjoint, bounded linear operators acting on a separable complex Hilbert space. We replace the weights $w_n=1$ in the classical unilateral shift $T$,…
We study the compact perturbations of an isometry on a separable Hilbert space and provide a complete characterization of when they are quasinormal. Based on that, we present a complete classification for a rank-one perturbation of a…
We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…
Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.
The two weight inequality for the Hilbert transform arises in the settings of analytic function spaces, operator theory, and spectral theory, and what would be most useful is a characterization in the simplest real-variable terms. We show…
We present strongly stable semi-discrete finite difference approximations to the quarter space problem (x>0, t>0) for the first order in time, second order in space wave equation with a shift term. We consider space-like (pure outflow) and…
In this paper we present necessary and sufficient conditions for the existence of a unique solution to the relaxed commutant lifting problem. The obtained conditions are more complicated than those for the classical commutant lifting…
We devote this paper to Hamburger type weighted shifts. We give in particular an affirmative answer to a problem concerning subnormality of the Aluthge transform of Hamburger moment measures with finite support. we also extend the notion…
We provide some new estimates for distances in harmonic function spaces of several variables related to mixed norm spaces.Some of them extend previously known assertions in this direction in the unit ball and upperhalfspace.
We consider weighted shift operators having the property of moment infinite divisibility; that is, for any $p > 0$, the shift is subnormal when every weight (equivalently, every moment) is raised to the $p$-th power. By reconsidering…
We give necessary and sufficient conditions for the sum of n subspaces of a Hilbert space to be closed. We also present various properties of n-tuples of subspaces with closed sum.
We say that a weighted shift $W_\alpha$ with (positive) weight sequence $\alpha: \alpha_0, \alpha_1, \ldots$ is {\it moment infinitely divisible} (MID) if, for every $t > 0$, the shift with weight sequence $\alpha^t: \alpha_0^t, \alpha_1^t,…
We characterize disjoint and simultaneously hypercyclic tuples of unilateral pseudo-shift operators on $\ell^p(\mathbb{N})$. As a consequence, complementing the results of Bernal and Jung, we give a characterization for simultaneously…
In this note, we shall overview some results related to ultraparacompactness and ultranormality in the general topological and point-free contexts. This note contains some standard results and counterexamples along with some results which…
Almost-commuting matrices with respect to the normalized Hilbert-Schmidt norm are considered. Normal almost commuting matrices are proved to be near commuting.
We study the spectral pictures of (jointly) hyponormal 2-variable weighted shifts with commuting subnormal components. By contrast with all known results in the theory of subnormal single and 2-variable weighted shifts, we show that the…
In this paper, we study an approximate controllability for the impulsive linear evolution equations in Hilbert spaces. The necessary and sufficient conditions for approximate controllability in terms of resolvent operators are given. An…
In this article, we investigate the ball version of von Neumann inequality for the class of doubly contractive $d$-tuple of weighted shift. We show that if the weighted shift is balanced or satisfies an appropriate weight condition, then it…
It is well known that subspaces of the Hardy space over the unit disk which are invariant under the backward shift occur as the image of an observability operator associated with a discrete-time linear system with stable state-dynamics, as…
The hyperinvariant subspace problem is solved in the setting of Hilbert and right Hamilton space, motivated by my earlier works in the invariant subspace problem.