相关论文: Time-Scaled Intertwining Cocycles and Identifiabil…

Recently the authors solved a long-standing problem and showed that for an arbitrary pair of contractions on Hilbert space with trace class difference has an integrable spectral shift function on the unit circle ${\Bbb T}$ and an analogue…

We consider a perturbed Floquet Hamiltonian $-i\partial_t + H + \beta V(\omega t)$ in the Hilbert space $L^2([0,T],E,dt)$. Here $H$ is a self-adjoint operator in $E$ with a discrete spectrum obeying a growing gap condition, $V(t)$ is a…

We investigate the spectrum of the generator induced on the space of Hilbert-Schmidt operators by a Gaussian quantum Markov semigroup with a faithful normal invariant state in the general case, without any symmetry or quantum detailed…

We study the spectral bounds of self-adjoint operators on the Hilbert space of square-integrable functions, arising from the representation theory of the Heisenberg group. Interestingly, starting either with the von Neumann lattice or the…

Let T be a C_{\cdot 0}-contraction on a Hilbert space H and S be a non-trivial closed subspace of H. We prove that S is a T-invariant subspace of H if and only if there exists a Hilbert space D and a partially isometric operator \Pi :…

We show that formal eigenvalue equations of analytic one-frequency Schr\"od-inger operators admit intrinsic analytic $Sp(2k,\C)$ structures, where $k=k(E)$ is the T-acceleration in global theory. For trigonometric potentials those…

We introduce a framework for implementing quantum operations as steady states of a subsystem in an extended Hilbert space. Each operation has a spectral criterion for reaching the steady state. This adds a `spectral switch' mechanism to the…

The paper investigates spectral properties of multi-interval Sturm-Liouville operators with distributional coefficients. Constructive descriptions of all self-adjoint and maximal dissipative/accumulative extensions in terms of boundary…

Motivated by Heisenberg's observable-only stance, we replace latent "information" (filtrations, hidden diffusions, state variables) with observable transitions between price states. On a discrete price lattice with a Hilbert-space…

We start with considering rank one self-adjoint perturbations $A_\alpha = A+\alpha(\,\cdot\,,\varphi)\varphi$ with cyclic vector $\varphi\in \mathcal{H}$ on a separable Hilbert space $\mathcal H$. The spectral representation of the…

Hamiltonian tridiagonal matrices characterized by multi-fractal spectral measures in the family of Iterated Function Systems can be constructed by a recursive technique here described. We prove that these Hamiltonians are almost-periodic.…

The topological Hochschild homology THH(R) of a commutative S-algebra (E_infty ring spectrum) R naturally has the structure of a commutative R-algebra in the strict sense, and of a Hopf algebra over R in the homotopy category. We show,…

An operator space analysis of quantum stochastic cocycles is undertaken. These are cocycles with respect to an ampliated CCR flow, adapted to the associated filtration of subspaces, or subalgebras. They form a noncommutative analogue of…

We construct commutative algebra spectra that represent the operator $K$-theory of $C^*$-algebras, which are algebras over the commutative ring spectra that represent topological $K$-theory. The spectral multiplicative structure introduces…

Motivated by the Freed-Hopkins-Teleman theorem we study graded equivariant higher twists of $K$-theory for the groups $G = SU(n)$ induced by exponential functors. We compute the rationalisation of these groups for all $n$ and all…

We show that (for the weak operator topology) the set of unitary operators on a separable infinite-dimensional Hilbert space is residual in the set of all contractions. The analogous result holds for isometries and the strong operator…

In this paper, we give the complete description of maps on self-adjoint bounded operators on Hilbert space which preserve a triadic relation involving the difference of operators and either commutativity or quasi-commutativity in both…

This article considers linear processes with values in a separable Hilbert space exhibiting long-range dependence. The scaling limits for the sample autocovariance operators at different time lags are investigated in the topology of their…

Subject of the paper deals with the perturbation theory of linear operators acting in Hilbert space. For a certain class of perturbations the question is considered about existence of transformation operators implementing linear similarity…

In the paper, we prove an analogue of the Kato-Rosenblum theorem in a semifinite von Neumann algebra. Let $\mathcal{M}$ be a countably decomposable, properly infinite, semifinite von Neumann algebra acting on a Hilbert space $\mathcal{H}$…