Related papers: Isometries of a Generalized Numerical Radius on Co…
Some preliminaries and basic facts regarding unbounded Wiener-Hopf operators (WH) are provided. WH with rational symbols are studied in detail showing that they are densely defined closed and have finite dimensional kernels and deficiency…
$(\mu;\nu)$-Hankel operators between separable Hilbert spaces were introduced and studied recently (\textit{$\mu$-Hankel operators on Hilbert spaces}, Opuscula Math., \textbf{41} (2021), 881--899). This paper, is devoted to generalization…
In the present paper, we provide several inequalities for the generalized numerical radius of operator matrices as introduced by A. Abu-omar and F. Kittaneh in [3]. We generalize the convexity and the log-convexity results obtained by M.…
Let $\Omega$ be a bounded convex Reinhardt domain in $\mathbb{C}^2$ and $\phi\in C(\bar{\Omega})$. We show that the Hankel operator $H_{\phi}$ is compact if and only if $\phi$ is holomorphic along every non-trivial analytic disc in the…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
In this article, we prove an inner product inequality for Hilbert space operators. This inequality, then, is utilized to present a general numerical radius inequality using convex functions. Applications of the new results include obtaining…
The purpose of this paper is to describe the Harnack parts for the operators of class C $\rho$ ($\rho$ \textgreater{} 0) on Hilbert spaces which were introduced by B. Sz. Nagy and C. Foias in [25]. More precisely, we study Harnack parts of…
This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including…
We show that any m-isometric tuples of commuting operators on a finite dimensional Hilbert space can be decomposed as a sum of a spherical isometry and a commuting nilpotent tuple. Our approach applies as well to tuples of algebraic…
We prove that for a right linear bounded normal operator on a quaternionic Hilbert space (quaternionic bounded normal operator) the norm and the numerical radius are equal. As a consequence of this result we give a new proof of the known…
In this article, we obtain several new weighted bounds for the numerical radius of a Hilbert space operator. The significance of the obtained results is the way they generalize many existing results in the literature; where certain values…
In this paper we study the theory of operators on complex Hilbert spaces, which achieve the norm in the unit sphere. We prove important results concerning the characterization of the AN operators, see Definition 1.2. The class of AN…
The article is devoted to the investigation of operators on a non locally compact group algebra. Their isomorphisms are also studied.
We study some basic properties of the class of universal operators on Hilbert space, and provide new examples of universal operators and universal pairs.
We define a function on the $C^{\ast}$-algebra of all bounded linear Hilbert space operators, which generalizes the operator radii, and we present some basic properties of this function. Our results extend several results in the literature.
We define the complete numerical radius norm for homomorphisms from any operator algebra into ${\mathcal B}({\mathcal H})$, and show that this norm can be computed explicitly in terms of the completely bounded norm. This is used to show…
Let $\mathcal{H}$ be a complex, separable Hilbert space and $\mathcal{B}(\mathcal{H})$ denote the algebra of all bounded linear operators acting on $\mathcal{H}$. Given a unitarily-invariant norm $\| \cdot \|_u$ on…
We show that the absolute numerical index of the space $L_p(\mu)$ is $p^{-1/p} q^{-1/q}$ (where $1/p+1/q=1$). In other words, we prove that $$ \sup\{\int |x|^{p-1}|Tx|\, d\mu \, : \ x\in L_p(\mu),\,\|x\|_p=1\} \,\geq \,p^{-\frac{1}{p}}…
We associate to any Riemannian symmetric space (of finite or infinite dimension) a L$^*$-algebra, under the assumption that the curvature operator has a fixed sign. L$^*$-algebras are Lie algebras with a pleasant Hilbert space structure.…
If a differential operator $D$ on a smooth Hermitian vector bundle $S$ over a compact manifold $M$ is symmetric, it is essentially self-adjoint and so admits the use of functional calculus. If $D$ is also elliptic, then the Hilbert space of…