Related papers: Eigenvalue estimates for the resolvent of a non-no…
In this paper, we present several new bounds for the norm and numerical radius of sums of Hilbert space operators. The obtained bounds form a new collection that enriches our understanding of these bounds. We compare our bounds with the…
In this article, the open problem of finding the exact value of the norm of the Hilbert matrix operator on weighted Bergman spaces $A^p_\alpha$ is adressed. The norm was conjectured to be $\frac{\pi}{\sin \frac{(2+\alpha)\pi}{p}}$ by…
The higher rank numerical range is closely connected to the construction of quantum error correction code for a noisy quantum channel. It is known that if a normal matrix $A \in M_n$ has eigenvalues $a_1, \..., a_n$, then its higher rank…
Parameter-elliptic boundary-value problems are investigated on the extended Sobolev scale. This scale consists of all Hilbert spaces that are interpolation spaces with respect to the Hilbert Sobolev scale. The latter are the H\"ormander…
The eigenvector-dependent nonlinear eigenvalue problem (NEPv) $A(P)V=V\Lambda$, where the columns of $V\in\mathbb{C}^{n\times k}$ are orthonormal, $P=VV^{\mathrm{H}}$, $A(P)$ is Hermitian, and $\Lambda=V^{\mathrm{H}}A(P)V$, arises in many…
We study random normal matrix models whose eigenvalues tend to be distributed within a narrow "band" around the unit circle of width proportional to $\frac1n$, where $n$ is the size of matrices. For general radially symmetric potentials…
Very recently, Bo\v{z}in and Karapetrovi\'c solved a conjecture by proving that the norm of the Hilbert matrix operator $\mathcal{H}$ on the Bergman space $A^p$ is equal to $\frac{\pi}{\sin(\frac{2\pi}{p})}$ for $2 < p < 4.$ In this article…
We study the spectral convergence of compact, self-adjoint operators on a separable Hilbert space under operator norm perturbations, and derive asymptotic expansions for their eigenvalues and eigenprojections. Our analysis focuses on…
This article is devoted to the spectral analysis of the electro-magnetic Schr\"odinger operator on the Euclidean plane. In the semiclassical limit, we derive a pseudo-differential effective operator that allows us to describe the spectrum…
We establish the convergence of pseudospectra in Hausdorff distance for closed operators acting in different Hilbert spaces and converging in the generalised norm resolvent sense. As an assumption, we exclude the case that the limiting…
A new approach to solving eigenvalue optimization problems for large structured matrices is proposed and studied. The class of optimization problems considered is related to computing structured pseudospectra and their extremal points, and…
For bounded linear operators $A,B$ on a Hilbert space $\mathcal{H}$ we show the validity of the estimate $$ \sum_{\lambda \in \sigma_d (B)} \dist(\lambda, \overline{\num}(A))^p \leq \| B-A \|_{\mathcal{S}_p}^p$$ and apply it to recover and…
We consider a family of random normal matrix models whose eigenvalues tend to occupy lemniscate type droplets as the size of the matrix increases. Under the insertion of a point charge, we derive the scaling limit at the singular boundary…
In this paper, we introduce the concept of Z$_1$-eigenvalue to infinite dimensional generalized Hilbert tensors (hypermatrix) $\mathcal{H}_\lambda^{\infty}=(\mathcal{H}_{i_{1}i_{2}\cdots i_{m}})$, $$ \mathcal{H}_{i_{1}i_{2}\cdots…
Let $A\in\mathbb{C}^{n\times n}$ and $\widetilde{A}\in\mathbb{C}^{n\times n}$ be two normal matrices with spectra $\{\lambda_{i}\}_{i=1}^{n}$ and $\{\widetilde{\lambda}_{i}\}_{i=1}^{n}$, respectively. The celebrated Hoffman--Wielandt…
We introduce compactness classes of Hilbert space operators by grouping together all operators for which the associated singular values decay at a certain speed and establish upper bounds for the norm of the resolvent of operators belonging…
We establish new integral inequalities for the numerical radius and the operator norm of bounded linear operators on Hilbert spaces. Our results refine classical triangle-type and operator matrix inequalities by incorporating convex…
For a pair of coupled rectangular random matrices we consider the squared singular values of their product, which form a determinantal point process. We show that the limiting mean distribution of these squared singular values is described…
We consider a general class of random matrices whose entries are centred random variables, independent up to a symmetry constraint. We establish precise high-probability bounds on the averages of arbitrary monomials in the resolvent matrix…
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded off-diagonal perturbation is studied. To this end, the optimization approach for general perturbations in [J. Anal. Math., to appear;…