Related papers: On Schatten restricted norms

Consider a Hilbert space obtained as the completion of the polynomials C[z} in m-variables for which the mnonomials are orthogonal. If the commuting weighted shifts defined by the coordinate functions are essentially normal, then the same…

For an unbounded operator $S$ on a Banach space the existence of invariant subspaces corresponding to its spectrum in the left and right half-plane is proved. The general assumption on $S$ is the uniform boundedness of the resolvent along…

Let $\mathcal{H}$ be a separable infinite-dimensional complex Hilbert space and let $\mathcal{J}$ be a two-sided ideal of the algebra of bounded operators $\mathcal{B}(\mathcal{H})$. The groups $\mathcal{G} \ell_\mathcal{J}$ and…

We study contractive projections, isometries, and real positive maps on algebras of operators on a Hilbert space. For example we find generalizations and variants of certain classical results on contractive projections on C*-algebras and…

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 give new inequalities for $A$-operator seminorm and $A$-numerical radius of semi-Hilbertian space operators and show that the inequalities obtained here generalize and improve on the existing ones. Considering a complex Hilbert space…

We consider linear bounded operators acting in Banach spaces with a basis, such operators can be represented by an infinite matrix. We prove that for an invertible operator there exists a sequence of invertible finite-dimensional operators…

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…

This paper is concerned with the convergence of power sequences and stability of Hilbert space operators, where "convergence" and "stability" refer to weak, strong and norm topologies. It is proved that an operator has a convergent power…

In this paper, we characterize the essential norm of Hankel operators from a weighted Fock space $F_{\varphi}^{p}$ to a weighted Lebesgue space $L_{\varphi}^{q}$ for all $1 \leq p, q < \infty$. Additionally, we characterize the Schatten-$h$…

A Hilbert space operator $S\in\B$ is left $m$-invertible by $T\in\B$ if $$\sum_{j=0}^m{(-1)^{m-j}\left(\begin{array}{clcr}m\\j\end{array}\right)T^jS^j}=0,$$ $S$ is $m$-isometric if…

Let $A\colon H\rightarrow H$ be a normal operator on an infinite-dimensional separable Hilbert space $H$ and let $S\subseteq H$ be a finite subset such that $\{A^nx\}_{n\geq 0,\,x\in S}$ can be rescaled to form a frame for $H$. That is,…

We extend the symbol calculus and study the limit operator theory for $\sigma$-compact, \'{e}tale and amenable groupoids, in the Hilbert space case. This approach not only unifies various existing results which include the cases of exact…

This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…

Let $X$ be a locally compact Hadamard space and $G$ be a totally disconnected group acting continuously, properly and cocompactly on $X$. We show that a closed subgroup of $G$ is amenable if and only if it is (topologically locally…

Utilizing the Birkhoff--James orthogonality, we present some characterizations of the norm-parallelism for elements of $\mathbb{B}(\mathscr{H})$ defined on a finite dimensional Hilbert space, elements of a Hilbert $C^*$-module over the…

A topological group $G$ is called extremely amenable if every continuous action of $G$ on a compact space has a fixed point. This concept is linked with geometry of high dimensions (concentration of measure). We show that a von Neumann…

We provide full characterisation of the Schatten properties of $[M_b,T]$, the commutator of Calder\'{o}n--Zygmund singular integral $T$ with symbol $b$ $(M_bf(x):=b(x)f(x))$ on stratified Lie groups $\mathbb{G}$. We show that, when $p$ is…

This note concerns uniform equicontinuity of families of operators on a separable Hilbert space H, and of families of maps on B(H). It is shown that a one parameter group of automorphisms is uniformly equicontinuous if and only if the group…

We study singular integral operators induced by $3$-dimensional Calder\'on-Zygmund kernels in the Heisenberg group. We show that if such an operator is $L^{2}$ bounded on vertical planes, with uniform constants, then it is also $L^{2}$…