相关论文: On circular Kippenhahn curves and the Gau-Wang-Wu …
Conditions are established for rank three partial isometries to have circular components contained in their Kippenhahn curves. In particular, such matrices with circular numerical ranges are described. It is also established that the…
This paper demonstrates the power of the calculus developed in the two previous parts of the series for all real forms of the almost Hermitian symmetric structures on smooth manifolds, including e.g. conformal Riemannian and almost…
In this paper, we are mainly concerned with studying arbitrary unbounded square roots of linear operators as well as some of their basic properties. The paper contains many examples and counterexamples. As an illustration, we give explicit…
We study matrices whose entries are free or exchangeable noncommutative elements in some tracial $W^*$-probability space. More precisely, we consider operator-valued Wigner and Wishart matrices and prove quantitative convergence to…
We investigate dynamical properties of linear operators that are obtained as the linearization of Lipschitz self-maps defined on a pointed metric space. These operators are known as Lipschitz operators. More concretely, for a Lipschitz…
In this note we discuss local gauge-invariant operators in noncommutative gauge theories. Inspired by the connection of these theories with the Matrix model, we give a simple construction of a complete set of gauge-invariant operators. We…
We show that if A is a Hilbert-space operator, then the set of all projections onto hyperinvariant subspaces of A, which is contained in the von Neumann algebra vN(A) that is generated by A, is independent of the representation of vN(A),…
In their LAMA'2016 paper Gau, Wang and Wu conjectured that a partial isometry $A$ acting on $\mathbb{C}^n$ cannot have a circular numerical range with a non-zero center, and proved this conjecture for $n\leq 4$. We prove it for operators…
We suppose that $G$ is a locally compact abelian group, $Y$ is a measure space, and $H$ is a reproducing kernel Hilbert space on $G\times Y$ such that $H$ is naturally embedded into $L^2(G\times Y)$ and it is invariant under the…
We consider a compact Riemann surface $\mathscr{R}$ with a complex of non-intersecting Jordan curves, whose complement is a pair of Riemann surfaces with boundary, each of which may be possibly disconnected. We investigate conformally…
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…
Given a Hilbert space operator $T$, the level sets of function $\Psi_T(z)=\|(T-z)^{-1}\|^{-1}$ determine the so-called pseudospectra of $T$. We set $\Psi_T$ to be zero on the spectrum of $T$. After giving some elementary properties of…
In this paper we study some geometric properties like parallelism, orthogonality and semi-rotundity in the space of bounded linear operators. We completely characterize parallelism of two compact linear operators between normed linear…
We study geometric properties of varieties associated with invariant subspaces of nilpotent operators. There are reductive algebraic groups acting on these varieties. We give dimensions of orbits of these actions. Moreover, a combinatorial…
We review the basic properties of effective actions of families of theories (i.e., the actions depending on additional non-perturbative moduli along with perturbative couplings), and their description in terms of operators (called…
Based on the success of a well-known method for solving higher order linear differential equations, a study of two of the most important mathematical features of that method, viz. the null spaces and commutativity of the product of…
We consider a Hilbert space that is a product of a finite number of Hilbert spaces and operators that are represented by "componental operators" acting on the Hilbert spaces that form the product space. We attribute operatorial properties…
We consider the Wigner matrix $W_{n}$ of dimension $n \times n$ as $n \to \infty$. The objective of this paper is two folds: first we construct an operator $\mathcal{W}$ on a suitable Hilbert space $\mathcal{H}$ and then define a suitable…
In this paper we present a systematic study of regular sequences of quasi-nonexpansive operators in Hilbert space. We are interested, in particular, in weakly, boundedly and linearly regular sequences of operators. We show that the type of…
We investigate a linear operator associated with a functional equation that arises from studying some class of invariant measures under multidimensional transformations. By examining its iterates, we derive an explicit solution formula for…