Related papers: Malnormal matrices

We show that every self--adjoint matrix B of trace 0 can be realized as B=T+T^* for a nilpotent matrix T of norm no greater than K times the norm of B, for a constant K that is independent of matrix size. More particularly, if D is a…

We prove that for every semigroup of Schwarz maps on the von~Neumann algebra of all bounded linear operators on a Hilbert space which has a subinvariant faithful normal state there exists an associated semigroup of contractions on the space…

A family of random matrices is said to converge strongly to a limiting family of operators if the operator norm of every noncommutative polynomial of the matrices converges to that of the limiting operators. Recent developments surrounding…

Several unitarily invariant norm inequalities and numerical radius inequalities for Hilbert space operators are studied. We investigate some necessary and sufficient conditions for the parallelism of two bounded operators. For a finite rank…

The paper considers some new properties of the so-called $A$-maximal numerical range of operators, denoted by $W_{\max}^A(\cdot)$, where $A$ is a positive bounded linear operator acting on a complex Hilbert space $\mathcal{H}$. Some…

We define the (convex) joint numerical range for an infinite family of compact operators in a Hilbert space H. We use this set to determine whether a self-adjoint compact operator A with {||A||, -||A||} in its spectrum is minimal respect to…

Let $H_1$ and $H_2$ be complex Hilbert spaces and $T:H_1\rightarrow H_2$ be a bounded linear operator. We say $T$ to be norm attaining, if there exists $x\in H_1$ with $\|x\|=1$ such that $\|Tx\|=\|T\|$. If for every closed subspace $M$ of…

In this paper, we consider an unbounded selfadjoint operator $A$ and its selfadjoint perturbations in the same Hilbert space $\mathcal{H}$. As S.Albeverio and P. Kurosov (2000), we call a selfadjoint operator $A_{1}$ the singular…

For $n$-normal operators $A$ [2, 4, 5], equivalently $n$-th roots $A$ of normal Hilbert space operators, both $A$ and $A^*$ satisfy the Bishop--Eschmeier--Putinar property $(\beta)_{\epsilon}$, $A$ is decomposable and the quasi-nilpotent…

We prove that every bounded self-adjoint operator in Hilbert space is a real linear combination of $4$ orthoprojections. Also we show that operators of the form identity minus compact positive operator can not be decomposed in a real linear…

Let $A_\N$ be the symmetric operator given by the restriction of $A$ to $\N$, where $A$ is a self-adjoint operator on the Hilbert space $\H$ and $\N$ is a linear dense set which is closed with respect to the graph norm on $D(A)$, the…

We provide several perturbation theorems regarding closable operators on a real or complex Hilbert space. In particular we extend some classical results due to Hess--Kato, Kato--Rellich and W\"ust. Our approach involves ranges of matrix…

In this paper, we study the linear mapping which sends the sequence $x=(x_n)_{n \in \mathbb{N}}$ to $y=(y_n)_{n \in \mathbb{N}}$ where $y_n = \sum_{k=1}^\infty f(n/k)x_k$ for $f: \mathbb{Q}^+ \to \mathbb{C}$. This operator is the…

This paper studies the diameter of the numerical range of bounded operators on Hilbert space and the induced seminorm, called the numerical diameter, on bounded linear maps between operator systems which is sensible in the case of unital…

Let $\mathbb{A}= \begin{pmatrix} A & 0 \\ 0 & A \\ \end{pmatrix} $ be a $2\times2$ diagonal operator matrix whose each diagonal entry is a bounded positive (semidefinite) linear operator $A$ acting on a complex Hilbert space $\mathcal{H}$.…

Let $E$ and $F$ be Hilbert $C^*$-modules over a $C^*$-algebra $\CAlg{A}$. New classes of (possibly unbounded) operators $t:E\to F$ are introduced and investigated. Instead of the density of the domain $\Def(t)$ we only assume that $t$ is…

We study inverse boundary problems for third-order nonlinear tensorial perturbations of biharmonic operators on a bounded domain in $\mathbb{R}^n$, where $n\geq 3$. By imposing appropriate assumptions on the nonlinearity, we demonstrate…

We initiate the study of matrix convexity for operator spaces. We define the notion of compact rectangular matrix convex set, and prove the natural analogs of the Krein-Milman and the bipolar theorems in this context. We deduce a canonical…

The main result of this paper is the extension of the Schur-Horn Theorem to infinite sequences: For two nonincreasing nonsummable sequences x and y that converge to 0, there exists a compact operator A with eigenvalue list y and diagonal…

Let $A$ be a bounded linear operator on a complex Banach space $X.$ For a given $\alpha \geq 0,$ we consider the class $\mathcal{D}_{A}^{\alpha }\left( \mathbb{R} \right) $ of all bounded linear operators $T$ on $X$ for which there exists a…