相关论文: Asymmetric Burkholder inequalities in noncommutati…
We investigate $\rho$-orthogonality and its local symmetry in the space of bounded linear operators. A characterization of Hilbert space operators with symmetric numerical range is established in terms of $\rho$-orthogonality. Further, we…
The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of…
We completely characterize the left-symmetric points, the right-symmetric points, and, the symmetric points in the sense of Birkhoff-James, in a Banach space. We obtain a complete characterization of the left-symmetric (right-symmetric)…
Normalized free semi-circular random variables satisfy an upper Khintchine inequality in $L_\infty$. We show that this implies the corresponding upper Khintchine inequality in any noncommutative Banach function space. As applications, we…
The global counterpart of infinitesimal symmetries of noncommutative space-time is discussed.
In this paper we solve several problems concerning joint similarity to n-tuples of operators in noncommutative varieties in $[B(\cH)^n]_1$ associated with positive regular free holomorphic functions in $n$ noncommuting variables and with…
We prove that operators satisfying the hypotheses of the extrapolation theorem for Muckenhoupt weights are bounded on weighted Morrey spaces. As a consequence, we obtain at once a number of results that have been proved individually for…
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…
In order to find a noncommutative analog of Schwarzschild or Schhwarzschild-de Sitter blackhole we investigate spherically symmetric spaces generated by four noncommutative coordinates in the frame formalism. We present two solutions which…
The objective of this paper is to introduce and study a complicated nonlinear system, called coupled variational-hemivariational inequalities, which is described by a highly nonlinear coupled system of inequalities on Banach spaces. We…
It is well known that subspaces of the Hardy space over the unit disk which are invariant under the backward shift occur as the image of an observability operator associated with a discrete-time linear system with stable state-dynamics, as…
We fully characterize those von Neumann algebras having the ball-covering property. We also study the ball-covering property of noncommutative symmetric spaces. In particular, we provide a number of new examples of non-separable…
This paper extends the known characterization of interpolation and sampling sequences for Bergman spaces to the mixed-norm spaces. The Bergman spaces have conformal invariance properties not shared by the mixed-norm spaces. As a result,…
50 years after Thompson's famous triangle inequality for the operator right modulus, we establish a triangle inequality for the quadratic symmetric modulus. We also discuss the corresponding equality cases as well as the…
Local boundedness and Harnack inequalities are studied for solutions to parabolic and elliptic integro-differential equations whose governing nonlocal operators are associated with nonsymmetric forms. We present two independent proofs, one…
The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically…
The aim of this paper is to begin a systematic study of functional inequalities on symmetric spaces of noncompact type of higher rank. Our first main goal of this study is to establish the Stein-Weiss inequality, also known as a weighted…
We study unitarily equivalent bilateral weighted shifts with operator weights. We establish a general characterization of unitary equivalence of such shifts under the assumption that the weights are quasi-invertible. We prove that under…
Skewing operators play a central role in the symmetric function theory because of the importance of the product structure of the symmetric function space. The theory of noncommutative symmetric functions is a useful tool for studying…
In this paper, we review the progress in the analysis of magnetic monopoles as generalized states in quantum mechanics. We show that the considered model contains rich algebraic structure that generates symmetries which have been utilized…