Related papers: The C-Numerical Range for Schatten-Class Operators

In the case of any bounded open set $\Omega$ $\subset$ R d with boundary $\partial$$\Omega$, we first construct a directional trace in any direction $\theta$ of the unit sphere, for any u $\in$ L 2 ($\Omega$) whose the directional…

Let $f=h+\overline{g}$ be a normalized harmonic mapping in the unit disk $\ID$. In this paper, we obtain the sharp radius of univalence, fully starlikeness and fully convexity of the harmonic linear differential operators…

Let $\mathcal{L}(\mathscr{H})$ denote the $C^*$-algebra of adjointable operators on a Hilbert $C^*$-module $\mathscr{H}$. We introduce the generalized Cauchy-Schwarz inequality for operators in $\mathcal{L}(\mathscr{H})$ and investigate…

In this article, a comprehensive study is made on the continuity, compactness, and spectrum of the lower triangular terraced matrix, introduced by H. C. Rhaly, Jr. [Houston J. Math. 15(1): 137-146, 1989], acting on the weighted null…

In this paper we study operators originated from semi-B-Fredholm theory and as a consequence we get some results regarding boundaries and connected hulls of the corresponding spectra. In particular, we prove that a bounded linear operator…

Let $\C$ denote the field of complex numbers, and fix a nonzero $q \in \C$ such that $q^4 \ne 1$. Define a $\C$-algebra $\Delta_q$ by generators and relations in the following way. The generators are $A,B,C$. The relations assert that each…

Let $H(\mathbb{C})$ be the set of all entire functions endowed with the topology of uniform convergence on compact sets. Let $\lambda,b\in\mathbb{C}$, let $C_{\lambda,b}:H(\mathbb{C})\to H(\mathbb{C})$ be the composition operator…

Let ${\bf R}$ denote any of the following classes: upper (lower) semi-Fredholm operators, Fredholm operators, upper (lower) semi-Weyl operators, Weyl operators, upper (lower) semi-Browder operators, Browder operators. For a bounded linear…

We generalise the Elliptical Range Theorem to characterise the numerical range of matrices belonging to a subspace of the space of \(3 \times 3\) matrices. Using Specht's Theorem, which characterizes when two matrices are unitarily…

We find the radius of starlikeness of order $\alpha$, $0\leq \alpha<1$, of normalized analytic functions $f$ on the unit disk satisfying either $\operatorname{Re}(f(z)/g(z))>0$ or $\left| (f(z)/g(z))-1\right|<1$ for some close-to-star…

Let $H$ be a separable Hilbert space with a fixed orthonormal basis. Let $\mathbb B^{(k)}(H)$ denote the set of operators, whose matrices have no more than $k$ non-zero entries in each line and in each column. The closure of the union (over…

Let $\mathcal{C}_p$ be the Schatten $p$-class for $p>0$. Generalizations of the parallelogram law for the Schatten 2-norms have been given in the following form: If $\mathbf{A}=\{A_1,A_2,...,A_n\}$ and $\mathbf{B}=\{B_1,B_2,...,B_n\}$ are…

We introduce a one-step cascade symmetric system whose local symmetry geometry is organized by finite $\rho$-closed windows and one-step stars rather than by rowwise-independent toggles. The resulting symmetric model isolates a new $ZF + DC…

We consider a non-self-adjoint $H$ given as the perturbation of a self-adjoint operator $H_0$. We suppose that $H$ is of the form $H=H_0+CWC$ where $C$ is a bounded, positive definite and relatively compact with respect to $H_0$, and $W$ is…

We introduce a class of (tuples of commuting) unbounded operators on a Banach space, admitting smooth functional calculi, that contains all operators of Helffer-Sj\"ostrand type and is closed under the action of smooth proper mappings.…

In this paper we compute the closure of the numerical range of certain periodic tridiagonal operators. This is achieved by showing that the closure of the numerical range of such operators can be expressed as the closure of the convex hull…

The goal of the paper is to study the particular class of regularly ${\mathcal{H}}$-convex functions, when ${\mathcal{H}}$ is the set ${\mathcal{L}\widehat{C}}(X,{\mathbb{R}})$ of real-valued Lipschitz continuous classically concave…

We link Sogge's type $L^p$-estimates for eigenfunctions of the Laplacian on compact manifolds with the problem of providing criteria for the $r$-nuclearity of Fourier integral operators. The classes of Fourier integral operators…

Let $\Omega$ be a bounded convex domain in $\mathbb{C}^{n}$, $n\geq 2$, $1\leq q\leq (n-1)$, and $\phi\in C(\bar{\Omega})$. If the Hankel operator $H^{q-1}_{\phi}$ on $(0,q-1)$--forms with symbol $\phi$ is compact, then $\phi$ is…

It is shown that the numerical range of a linear operator operator in a Hilbert space is a (complete) $(1{+}\sqrt2)$-spectral set. The proof relies, among other things, in the behavior of the Cauchy transform of the conjugates of…