Related papers: Convex domains and K-spectral sets

We describe all isometries of the $q$-numerical radius on the space ${\mathcal K}(\mathcal H)$ of compact operators on a (possibly infinite-dimensional) Hilbert space $\mathcal H$.

By means of the operator extension theory, we construct an explicitly solvable model of a simple-cubic three-dimensional regimented array of quantum dots in the presence of a uniform magnetic field. The spectral properties of the model are…

We consider an infinite dimensional separable Hilbert space and its family of compact integrable cocycles over a dynamical system f. Assuming that f acts in a compact Hausdorff space X and preserves a Borel regular ergodic measure which is…

The higher-rank numerical range is a convex compact set generalizing the classical numerical range of a square complex matrix, first appearing in the study of quantum error correction. We will discuss some of the real algebraic and convex…

Consider a bounded strongly pseudo-convex domain $\Omega $ with a smooth boundary in $\mathbb{C}^n$. Let $\mathcal{T}$ be the Toeplitz algebra on the Bergman space $L^2_a(\Omega )$. That is, $\mathcal{T}$ is the $C^\ast $-algebra generated…

Concerning the Laplace operator with homogeneous Dirichlet boundary conditions, the classical notion of isospectrality assumes that two domains are related when they give rise to the same spectrum. In two dimensions, non isometric,…

We provide a detailed description of the model Hilbert space $L^2(\bbR; d\Sigma; \cK)$, were $\cK$ represents a complex, separable Hilbert space, and $\Sigma$ denotes a bounded operator-valued measure. In particular, we show that several…

We extend the notion of a spectral triple to that of a higher-order relative spectral triple, which accommodates several types of hypoelliptic differential operators on manifolds with boundary. The bounded transform of a higher-order…

In a Riemannian manifold a regular convex domain is said to be $\lambda$-convex if its normal curvature at each point is greater than or equal to $\lambda$. In a Hadamard manifold, the asymptotic behaviour of the quotient…

In this papers we investigate the g-frame and Bessel g-sequence related to a linear bounded operator $K$ in Hilbert $C^{\ast}$-module and we establish some results.

Real linear operators between two complex Banach spaces unify naturally two important classes of linear operators and antilinear operators. We give a survey of basic geometric, spectral and duality properties of real linear operators. The…

As needed for the construction of rank $n$ continuous frames on a right quaternionic Hilbert space the so-called S-spectrum of a right quaternionic operator is studied. Using the S-spectrum, as for the case of complex Hilbert spaces, along…

We prove in this paper that the Hilbert geometry associated with an open convex polygonal set is Lipschitz equivalent to Euclidean plane.

For any bounded convex domain $\Omega$ with $C^{2}$ boundary in $\mathbb{C}^{n}$, we show that there exist positive constants $C_{1}$ and $C_{2}$ such that \[ C_{1}\sqrt{\dfrac{K\left(w,w\right)}{\delta\left(w\right)}}\leq\left\Vert…

Given a subspace $U\subset\mathbb{C}[x_1,\dots,x_n]_d$ we consider the closure of the image of the rational map $\mathbb{P}^{n-1}\dashrightarrow\mathbb{P}^{\dim U-1}$ given by $U$. Its coordinate ring is isomorphic to $\bigoplus_{i\ge 0}…

Let $\Omega$ be a strongly pseudoconvex domain. We introduce the Mabuchi space of strongly plurisubharmonic functions in $\Omega$. We study metric properties of this space using Mabuchi geodesics and establish regularity properties of the…

We characterize Hilbert-Schmidt Hankel operators on the Bergman spaces of smooth bounded strongly pseudoconvex domains in $\mathbb{C}^n$ for $n \geq 2$. We consider harmonic symbols of class $C^3$ up to the closure of the domain and show…

We obtaine the full characterization of proper closed invariant subspaces of a generalized backward shift operator (Pommiez operator) in the Frechet space of all holomorphic functions on a simply connected domain $\Omega$ of the complex…

A property of smooth convex domains $\Omega \subset \mathbb{R}^n$ is that if two points on the boundary $x, y \in \partial \Omega$ are close to each other, then their normal vectors $n(x), n(y)$ point roughly in the same direction and this…

Let E be a natural operator associated to the curvature tensor of a pseudo-Riemannian manifold. This survey article studies when the spectrum, or more generally the real Jordan normal form, of E is constant on the natural domain of…