Related papers: Frames and operators in Schatten classes

The bilateral shift operator $B$ has been the mainstay of stationary process modeling whereas we argue that the unilateral shift operator $T$ may be better suited to analyze invertibility. While doing so, we partially unify the notion of…

We extend results on compressed Toeplitz operators on the backward shift invariant subspaces of $H^2 $ to the context of the spaces $H^p$, $1<p<\infty.$

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…

In topological equivalence, a bounded linear operator between Banach spaces - we focus on the case of Hilbert spaces - is viewed as only acting linearly and continuously between them qua different spaces with the structure of linear…

We define positive Toeplitz operators between harmonic Bergman-Besov spaces $b^p_\alpha$ on the unit ball of $\mathbb{R}^n$ for the full ranges of parameters $0<p<\infty$, $\alpha\in\mathbb{R}$. We give characterizations of bounded and…

We establish, for $1 < p < \infty$, higher order $\mathcal{S}^p$-differentiability results of the function $\varphi : t\in \mathbb{R} \mapsto f(A+tK) - f(A)$ for selfadjoint operators $A$ and $K$ on a separable Hilbert space $\mathcal{H}$…

In this paper, we focus on the weighted Bergman spaces $A_{\varphi}^{p}$ in $\mathbb{D}$ with $\varphi\in\mathcal{W}_{0}$. We first give characterizations of those finite positive Borel measures $\mu$ in $\mathbb{D}$ such that the embedding…

This paper resolves a number of conjectures in the perturbation theory of linear operators. Namely, we prove that every Lipschitz function is operator Lipschitz in the Schatten-von Neumann ideals $S^\alpha$, $1 < \alpha < \infty$. The…

We characterize classes of linear maps between operator spaces $E$, $F$ which factorize through maps arising in a natural manner via the Pisier vector-valued non-commutative $L^p$ spaces $S_p[E^*]$ based on the Schatten classes on the…

Let $E$ and $B$ be arbitrary weakly compact JB$^*$-triples whose unit spheres are denoted by $S(E)$ and $S(B)$, respectively. We prove that every surjective isometry $f: S(E) \to S(B)$ admits an extension to a surjective real linear…

We study the learnability of a class of compact operators known as Schatten--von Neumann operators. These operators between infinite-dimensional function spaces play a central role in a variety of applications in learning theory and inverse…

We determine the Schatten class for the compact resolvent of Dirichlet realizations, in unbounded domains, of a class of non-selfadjoint differential operators. This class consists of operators that can be obtained via analytic dilation…

We prove a Tb Theorem that characterizes all Calderon-Zygmund operators that extend compactly on L^p(R^n), 1<p<\infty . The result, whose proof does not require the property of accretivity, can be used to prove compactness of the Double…

The Invariant Subset Problem on the Hilbert space is to know whether there exists a bounded linear operator $T$ on a separable infinite-dimensional Hilbert space $H$ such that the orbit $\{T^{n}x;\ n\ge 0\}$ of every non-zero vector $x\in…

We introduce compactness classes of Hilbert space operators by grouping together all operators for which the associated singular values decay at a certain speed and establish upper bounds for the norm of the resolvent of operators belonging…

Let $0<p,q\leq \infty$ and denote by $\mathcal{S}_p^N$ and $\mathcal{S}_q^N$ the corresponding Schatten classes of real $N\times N$ matrices. We study the Gelfand numbers of natural identities $\mathcal{S}_p^N\hookrightarrow…

This is a continuation of our previous research about an oscillatory integral operator $T_{\alpha, \beta}$ on compact manifolds $\mathbb{M}$. We prove the sharp $H^{p}$-$L^{p,\infty}$ boundedness on the maximal operator $T^{*}_{\alpha,…

This paper studies the \(k^{th}-\)order slant Toeplitz and slant little Hankel operators on the weighted Bergman space \(\mathcal{A}_\alpha^2(\mathbb{D})\). These operators are constructed using a slant shift operator \(W_k\) composed with…

We investigate the Schatten-class properties of pseudo-differential operators with the (revisted) method of Cordes and Kato. As symbol classes we use classes similar to those of Cordes in which the $L^{\infty}$% -conditions are replaced by…

A Helson matrix is an infinite matrix $A = (a_{m,n})_{m,n\geq1}$ such that the entry $a_{m,n}$ depends only on the product $mn$. We demonstrate that the orthogonal projection from the Hilbert--Schmidt class $\mathcal{S}_2$ onto the subspace…