Related papers: Schatten classes and commutator in the two weight …

We characterize the weak-type boundedness of the Hilbert transform $H$ on weighted Lorentz spaces $\Lambda^p_u(w)$, with $p>0$, in terms of some geometric conditions on the weights $u$ and $w$ and the weak-type boundedness of the…

This is a continuation of our paper \cite{AP2}. We prove that for functions $f$ in the H\"older class $\L_\a(\R)$ and $1<p<\be$, the operator $f(A)-f(B)$ belongs to $\bS_{p/\a}$, whenever $A$ and $B$ are self-adjoint operators with…

Let R: V x V -> V x V be a Hecke type solution of the quantum Yang-Baxter equation (a Hecke symmetry). Then, the Hilbert-Poincre' series of the associated R-exterior algebra of the space V is a ratio of two polynomials of degree m…

Gelfand duality between unital commutative C*-algebras and Compact Hausdorff spaces is extended to all unital C*-algebras, where the dual objects are what we call compact Hausdorff quantum spaces. We apply this result to obtain, a…

A pseudo-Hermitian coupled-channel square-well model is proposed, solved and discussed. The domain of parameters is determined where all the bound-state energies (twice degenerate with respect to the second observable which we call "spin")…

The translation of an operator is defined by using conjugation with time-frequency shifts. Thus, one can define $\Lambda$-shift-invariant subspaces of Hilbert-Schmidt operators, finitely generated, with respect to a lattice $\Lambda$ in…

This paper is the second in a series exploring the properties of a functor which assigns a homotopy double groupoid with connections to a Hausdorff space. We show that this functor satisfies a version of the van Kampen theorem, and so is a…

This paper investigates the shadowing properties in semi-hyperbolic systems. We introduce three classes of shadowing properties defined on families of manifolds, and prove that a semi-hyperbolic family possesses the $L^p$ bi-shadowing…

This note is devoted to the study of Hyt\"{o}nen's extrapolation theorem of compactness on weighted Lebesgue spaces. Two criteria of compactness of linear operators in the two-weight setting are obtained. As applications, we obtain…

We prove that the class of Muckenhoupt A_p weights coincides with the intersection of finitely many suitable translates of dyadic A_p, in both the one-parameter and multiparameter cases, and that the analogous results hold for the reverse…

The Hilbert transform has a linear bound in the $A_{2}$ characteristic on weighted $L^{2}$, \begin{equation*} \left\Vert H\right\Vert _{L^{2}(w)\rightarrow L^{2}(w)}\lesssim \left[ w \right] _{A_{2}}, \end{equation*} and we extend this…

Following the theory of principal $\infty$-bundles of Niklaus-Schreiber-Steveson, we develop a homotopy categorification of Hopf algebras, which model quantum groups. We study their higher-representation theory in the setting of…

In the two-Higgs-doublet model, different Higgs doublets can be viewed as components of a generic "hyperspinor". We decompose the Higgs potential of this model into irreducible representations of the SU(2) group of transformations of this…

Let $(S_1, S_2)$ be a bi-isometry, that is, a pair of commuting isometries $S_1$ and $S_2$ on a complex Hilbert space $\mathscr H.$ By the von Neumann-Wold decomposition, the hyper-range $\mathscr H_\infty(S_1):=\cap_{n=0}^\infty…

In a previous paper we generalized the theory of W*-modules to the setting of modules over nonselfadjoint dual operator algebras, obtaining the class of weak*-rigged modules. At that time we promised a forthcoming paper devoted to other…

We construct a class of representations of the Heisenberg algebra in terms of the complex shift operators subject to the proper continuous limit imposed by the correspondence principle. We find a suitable Hilbert space formulation of our…

In this paper, we study one of the fundamental notions in dynamical systems, the shadowing of invertible (bounded and linear) operators on a Hilbert space. Although the problem of finding a spectral characterization for shadowing has been…

We present some old and new results on a class of invariant spaces of holomorphic functions on symmetric domains, both in their circular bounded realizations and in their unbounded realizations as Siegel domains of type II. These spaces…

In this paper we study subspaces which are invariant under squares and cubes (separately as well as jointly) of unicellular backward weighted shift operators on a separable Hilbert space. The finite-dimensional subspaces are characterized…

Let $\M$ be a finite von Neumann algebra acting on a Hilbert space $\H$ and $\AA$ be a transitive algebra containing $\M'$. In this paper we prove that if $\AA$ is 2-fold transitive, then $\AA$ is strongly dense in $\B(\H)$. This implies…