Related papers: The structure of twisted power partial isometries

In this work, we stress the existence of isomorphisms which map complex contours from the upper half to contours in the lower half of the complex plane. The metric operator is found to depend on the chosen contour but the maps connecting…

We show that partial transposition for pure and mixed two-particle states in a discrete $N$-dimensional Hilbert space is equivalent to a change in sign of a "momentum-like" variable of one of the particles in the Wigner function for the…

Let $N$ be a weakly unitarily invariant norm (i.e. invariant for the coadjoint action of the unitary group) in the space of skew-Hermitian matrices $\mathfrak{u}_n(\mathbb C)$. In this paper we study the geometry of the unit sphere of such…

The celebrated theorem of Berger, Coburn and Lebow on pairs of commuting isometries can be formulated as follows: a pure isometry $V$ on a Hilbert space $\mathcal{H}$ is a product of two commuting isometries $V_1$ and $V_2$ in…

In this article we show how certain irreducible unitary representation $ \Pi_\lambda $ of the twisted Heisenberg group $ \He_\lambda^n(\C)$ leads to the twisted modulation spaces $ M_\lambda^{p,q}(\R^{2n}).$ These $ \Pi_\lambda $ also turn…

In this paper first we give a partial answer to a question of L. Moln\'ar and W. Timmermann. Namely, we will describe those linear (not necessarily bijective) transformations on the set of self-adjoint matrices which preserve a unitarily…

Let $A$ be a bounded, injective and self-adjoint linear operator on a complex separable Hilbert space. We prove that there is a pure isometry, $V$, so that $AV>0$ and $A$ is Hankel with respect to $V$, i.e. $V^*A = AV$, if and only if $A$…

Let H_0 (resp. H_\infty denote the class of commuting pairs of subnormal operators on Hilbert space (resp. subnormal pairs), and for an integer k>=1 let H_k denote the class of k-hyponormal pairs in H_0. We study the hyponormality and…

Motivated by questions raised in the preprint [AL20] by Accardi and Lu (private communication), we examine criteria for when the product of two partial isometries between Hilbert spaces is again a partial isometry and we use this to define…

This paper introduces and investigates the class of \textit{$k$-quasi $n$-power posinormal operators} in Hilbert spaces, generalizing both posinormal and $n$-power posinormal operators. We establish fundamental properties including matrix…

In the recent progress [BE1], [M], [Z1] and [Z2], the well-known Jacobian conjecture ([BCW], [E]) has been reduced to a problem on HN (Hessian nilpotent) polynomials (the polynomials whose Hessian matrix are nilpotent) and their (deformed)…

Let $G$ be a group. An element $g$ in $G$ is called reversible if it is conjugate to $g^{-1}$ within $G$, and called strongly reversible if it is conjugate to its inverse by an order two element of $G$. Let $\textbf{H}_{\mathbb H}^n$ be the…

This paper examines chains of $N$ coupled harmonic oscillators. In isolation, the $j$th oscillator ($1\leq j\leq N$) has the natural frequency $\omega_j$ and is described by the Hamiltonian $\frac{1}{2}p_j^2+\frac{1}{2}\omega_j^2x_j^2$. The…

Using a new manner to rescale fields in $\mathcal{N}=2$ gauged supergravity with n$_{V}$ vector multiplets and n$_{H}$ hypermultiplets, we develop the explicit derivation of the rigid limit of quaternionic isometry Ward identities agreeing…

A commuting $n$-tuple $(T_1, \ldots, T_n)$ of bounded linear operators on a Hilbert space $\clh$ associate a Hilbert module $\mathcal{H}$ over $\mathbb{C}[z_1, \ldots, z_n]$ in the following sense: \[\mathbb{C}[z_1, \ldots, z_n] \times…

For every point on the Jacobian of the modular curve $X_0(l)$ we define and study certain twisted holomorphic Eisenstein series. These are particular cases of a more general notion of twisted modular forms which correspond to sections on…

We study topologization of the semigroup $\mathscr{O\!\!I}\!_n(L)$ of finite partial order isomorphisms of a bounded rank of an infinite linear ordered set $(L,\leqslant)$. In particular we show that every $T_1$ left-topological…

Multidimensional Heisenberg algebras, whose creation and annihilation operators are the N-dimensional vectors, can be injected into simple Lie algebras g. It is demonstrated that the spectrum of their deformations can be investigated using…

Every almost Hermitian structure $(g,J)$ on a four-manifold $M$ determines a hypersurface $\Sigma_J$ in the (positive) twistor space of $(M,g)$ consisting of the complex structures anti-commuting with $J$. In this note we find the…

For commuting contractions $T_1,\dots ,T_n$ acting on a Hilbert space $\mathcal H$ with $T=\prod_{i=1}^n T_i$, we find a necessary and sufficient condition under which $(T_1,\dots ,T_n)$ dilates to commuting isometries $(V_1,\dots ,V_n)$ on…