Related papers: Discrete Translates of an Operator in the Schatten…

We study those operators on a Hilbert space that can be lifted / extended to any twisted Hilbert space. We prove that these form an ideal of operators which contains all the Schatten classes. We characterize those multiplication operators…

We introduce and study a class of operator tuples in complex Hilbert spaces, which we call spherical tuples. In particular, we characterize spherical multi-shifts, and more generally, multiplication tuples on RKHS. We further use these…

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 study operators of the form X+Y where Y has a finite p-th Schatten norm (p<2), and X is self-adjoint and of Hilbert-Schmidt class. Our study is based on new theorems on zero distribution of entire functions of finite order.

Let $\mathcal{C}_p$ be the Schatten $p$-class for $p>0$. Generalizations of the parallelogram law for the Schatten 2-norms have been given in the following form: If $\mathbf{A}=\{A_1,A_2,...,A_n\}$ and $\mathbf{B}=\{B_1,B_2,...,B_n\}$ are…

Fourier integral operators with sufficiently smooth phase act on the time-frequency content of functions. However time-frequency analysis has only recently been used to analyze these operators. In this paper, we show that if a Fourier…

In this paper we continue our program of revisiting the new aspects about the boundedness properties of pseudo-differential operators on the torus. Here we prove $H^p$-$L^p$ and $H^p$-estimates for H\"ormander classes of pseudo-differential…

In this paper we use Riesz spectral Theory and Gershgorin Theory to obtain explicit information concerning the spectrum of pseudo-differential operators defined on the unit circle $\mathbb{T} := \mathbb{R}/ 2 \pi \mathbb{ Z}$. For symbols…

We show that many invariant subspaces M for d-shifts (S_1,...,S_d) of finite rank have the property that the projection P onto M almost commutes with the S_k in the sense that the commutators PS_k - S_kP belong to the Schatten-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…

Let $A_1, ... A_n$ be operators acting on a separable complex Hilbert space such that $\sum_{i=1}^n A_i=0$. It is shown that if $A_1, ... A_n$ belong to a Schatten $p$-class, for some $p>0$, then 2^{p/2}n^{p-1} \sum_{i=1}^n \|A_i\|^p_p \leq…

We address the question of describing the membership to Schatten-Von Neumann ideals $\mathcal{S}_ p$ of integration operators $(T_ g f)(z)=\int_{0}^{z}f(\zeta)\,g'(\zeta)\,d\zeta$ acting on Dirichlet type spaces. We also study this problem…

In this work we study Schatten-von Neumann classes of tensor products of invariant operators on Hilbert spaces. In the first part we first deduce some spectral properties for tensors of anharmonic oscillators thanks to the knowledge on…

We investigate the Schatten-von Neumann properties of pseudo-differential operators using the method proposed by A. Boulkhemair in \cite{Boulkhemair 2}. The symbols are elements of the ideals $S_{w}^{p}$ of the Sj\"ostrand algebra $S_{w}$.

Let $P_\gamma$ be the orthogonal projection from the space $L ^2 (\mathbb{B}_n, dv_\gamma)$ to the standard weighted Bergman space $L_a ^2 (\mathbb{B}_n, dv_\gamma)$. In this paper, we characterize the Schatten $p$ class membership of the…

We establish continuity and Schatten-von Neumann properties for matrix operators with matrices satisfying mixed quasi-norm estimates. These considerations also include the case when the Lebesgue and Schatten parameters are allowed to stay…

We study unconditional subsequences of the canonical basis e_rc of elementary matrices in the Schatten class S^p. They form the matrix counterpart to Rudin's Lambda(p) sets of integers in Fourier analysis. In the case of p an even integer,…

Let $G$ be a locally compact group with left regular representation $\lambda_{G}.$ We say that $G$ admits a frame of translates if there exist a countable set $\Gamma\subset G$ and $\varphi\in L^{2}(G)$ such that $(\lambda_{G}(x)…

In this work we establish sharp kernel conditions ensuring that the corresponding integral operators belong to Schatten-von Neumann classes. The conditions are given in terms of the spectral properties of operators acting on the kernel. As…

In this paper we introduce the Schatten class of operators and the Berezin transform of operators in the quaternionic setting. The first topic is of great importance in operator theory but it is also necessary to study the second one…