相关论文: Noncommutative analysis of Hermite expansions
It is known that, for a positive Dunford-Schwartz operator in a noncommutative $L^p$-space, $1\leq p<\infty$, or, more generally, in a noncommutative Orlicz space with order continuous norm, the corresponding ergodic averages converge…
In the present paper, we establish that Riesz transforms for Dunkl Hermite expansion as introduced in [4] are singular integral operators with H\"ormander's type conditions and we show that are bounded on $L^p(\mathbb{R}^d; d\mu_k) 1 < p <…
In this paper we introduce Schwartz operators as a non-commutative analog of Schwartz functions and provide a detailed discussion of their properties. We equip them in particular with a number of different (but equivalent) families of…
We explicitly describe the Haagerup and the Kosaki non-commutative $L^p$-spaces associated with a tensor product von Neumann algebra $M_1\bar{\otimes}M_2$ in terms of those associated with $M_i$ and usual tensor products of unbounded…
Examples are given of non-Hermitian Hamiltonian operators which have a real spectrum. Some of the investigated operators are expressed in terms of the generators of the Weil-Heisenberg algebra. It is argued that the existence of an…
In this paper, we study the nonexpansive properties of metric resolvent, and present a convergence rate analysis for the associated fixed-point iterations (Banach-Picard and Krasnosel'skii-Mann types). Equipped with a variable metric, we…
It is known that, for a positive Dunford-Schwartz operator in a noncommutative $L^p-$space, $1\leq p<\infty$ or, more generally, in a noncommutative Orlicz space with order continuous norm, the corresponding ergodic averages converge…
Let $E$ be an operator space in the sense of the theory recently developed by Blecher-Paulsen and Effros-Ruan. We introduce a notion of $E$-valued non commutative $L_p$-space for $1 \leq p < \infty$ and we prove that the resulting operator…
We prove weak type inequalities for a large class of noncommutative square functions. In conjunction with BMO type estimates, interpolation and duality, we will obtain the corresponding equivalences in the whole Lp scale. The main novelty…
Aim of this paper is trying to show the possible significance, and usefulness, of various non-selfadjoint operators for suitable Observables in non-relativistic and relativistic quantum mechanics, and in quantum electrodynamics: More…
The study of Koopman and Liouville operators over reproducing kernel Hilbert spaces (RKHSs) has been gaining considerable interest over the past decade. In particular, these operators represent nonlinear dynamical systems, and through the…
A variety of physical phenomena, such as amplification, absorption, and radiation, can be effectively described using non-Hermitian operators. However, the introduction of non-uniform non-Hermiticity can lead to the formation of exceptional…
We study monotone operators in reflexive Banach spaces that are invariant with respect to a group of suitable isometric isomorphisms and we show that they always admit a maximal extension which preserves the same invariance. A similar…
In this paper we characterize the Lebesgue Bochner spaces $L^p(\mathbb{R}^n,B)$, $1<p<\infty$, by using Littlewood-Paley $g$-functions in the Hermite setting, provided that $B$ is a UMD Banach space. We use $\gamma$-radonifying operators…
We consider the reduction of problems on general noncommutative $L_p$-spaces to the corresponding ones on those associated with finite von Neumann algebras. The main tool is a unpublished result of the first named author which approximates…
This is a continuation of recent work on the general definition of pseudo-differential operators of type $1,1$, in H\"ormander's sense. Continuity in $L_p$-Sobolev spaces and H\"older--Zygmund spaces, and more generally in Besov and…
In [11], employing the technique of noncommutative interpolation, a maximal ergodic theorem in noncommutative Lp-spaces, 1 < p < infinity, was established and, among other things, corresponding maximal ergodic inequalities and individual…
Our first result is a noncommutative form of Jessen/Marcinkiewicz/Zygmund theorem for the maximal limit of multiparametric martingales or ergodic means. It implies bilateral almost uniform convergence with initial data in the expected…
We provide the conditions for the boundedness of the Bochner-Riesz operator acting between two different Grand Lebesgue Spaces. Moreover we obtain a lower estimate for the constant appearing in the Lebesgue-Riesz norm estimation of the…
Recently, the extrapolation theory has become a mainsteam method to investigate some integral type operators, since it does not depend on the density of spaces. The purpose of this paper is threefold. The first is to establish product…