相关论文: Local automorphisms of some quantum mechanical str…

In this paper we study a new class of transformations on the set of all Hilbert space effects. This consists of the bijective maps which preserve the order and zero product in both directions. The main result of the paper gives a complete…

In this paper we give necessary and sufficient conditions for a bounded linear Hilbert space operator to be an $m$-isometry for an unspecified $m$ written in terms of conditions that are applied to "one vector at a time". We provide…

We prove that every finite group $G$ can be realized as the automorphism group of a poset with $4|G|$ points. We also provide bounds for the minimum number of points of a poset with cyclic automorphism group of a given prime power order.

We define various notions of locality for *-automorphisms of the algebra of observables for an infinitely extended quantum spin system and study their relationship. In particular, we show that the ubiquitous characterization which arises…

We show that with few exceptions every local isometric automorphism of the group algebra $L^p(G)$ of a compact group $G$ is an isometric automorphism.

A finite dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator…

Let $X$ be a smooth projective hypersurface of dimension at least three. We show that every automorphism of the Hilbert square $X^{[2]}$ of $X$ is induced by some automorphism of $X$.

We give a necessary and sufficient condition for an automorphism of the Hilbert scheme of points on a K3 surface (non necessarily algebraic) to be induced by an automorphism of the surface. We prove furthermore that the group of birational…

In the present paper derivations and *-automorphisms of algebras of unbounded operators over the ring of measurable functions are investigated and it is shown that all L^0-linear derivations and L^{0}-linear *-automorphisms are inner.…

We study automorphism groups and birational automorphism groups of compact complex surfaces. We show that the automorphism group of such surface $X$ is always Jordan, and the birational automorphism group is Jordan unless $X$ is birational…

In functional analysis, approximative properties of an object become precise in its ultrapower. We discuss this idea and its consequences for automorphisms of II_1 factors. Here are some sample results: (1) an automorphism is approximately…

We give a classification of all non-symplectic automorphisms of prime order p acting on irreducible holomorphic symplectic fourfolds deformation equivalent to the Hilbert scheme of two points on a K3 surface, for p=2,3 and 7\leq p \leq 19.…

Let $A$ be a finite-dimensional algebra over a field $F$ with char$(F)\ne 2$. We show that a linear map $D:A\to A$ satisfying $xD(x)x\in [A,A]$ for every $x\in A$ is the sum of an inner derivation and a linear map whose image lies in the…

The aim of this paper is to show that if an order preserving bijective transformation of the Hilbert space effect algebra also preserves the probability with respect to a fixed pair of mixed states, then it is an ortho-order automorphism. A…

We study automorphisms of smooth hypersurfaces in projective space $\mathbb{P}^{n+1}$ whose fixed loci have codimension at most two for $n\geq2$. While classifications of possible orders of automorphisms are known, our aim is to explore the…

We determine the ring structure of the equivariant quantum cohomology of the Hilbert scheme of points in the complex plane. The operator of quantum multiplication by the divisor class is a nonstationary deformation of the quantum…

Bergman has given the following abstract characterisation of the inner automorphisms of a group $G$: they are exactly those automorphisms of $G$ which can be extended functorially along any homomorphism $G \rightarrow H$ to an automorphism…

Let $H$ be a separable real Hilbert space. Denote by ${\mathcal G}_{\infty}(H)$ the Grassmannian consisting of closed subspaces with infinite dimension and codimension. This Grassmannian is partially ordered by the inclusion relation. We…

Let G be a locally compact group, and let U be its unitary representation on a Hilbert space H. Endow the space L(H) of linear bounded operators on H with weak operator topology. We prove that if U is a measurable map from G to L(H) then it…

Let $R$ be a commutative, indecomposable ring with identity and $(P,\le)$ a partially ordered set. Let $FI(P)$ denote the finitary incidence algebra of $(P,\le)$ over $R$. We will show that, in most cases, local automorphisms of $FI(P)$ are…