Related papers: A non-injective version of Wigner's theorem

Let G be a group, Fin the family of its finite subgroups, and E(G,Fin) the classifying space. Let L^1 be the algebra of trace-class operators in an infinite dimensional, separable Hilbert space over the complex numbers. Consider the…

We propose an algorithm which for any recursive group $G$, given by its effectively enumerable generators and recursively enumerable relations, outputs an explicit embedding of $G$ into a finitely presented group directly written by its…

We construct operator systems $\mathfrak C_I$ that are universal in the sense that all operator systems can be realized as their quotients. They satisfy the operator system lifting property. Without relying on the theorem by Kirchberg, we…

The aim of this note is to understand the injectivity of Feigin's map $\mathbf{F_w}$ by representation theory of quivers, where $\mathbf{w}$ is the word of a reduced expression of the longest element of a finite Weyl group. This is achieved…

Consider a finite-dimensional real vector space equipped with a finite group acting unitarily on it. We address the general problem of constructing Euclidean stable embeddings of the quotient space of orbits. Our approach is based on…

Wigner's theorem asserts that an isometric (probability conserving) transformation on a quantum state space must be generated by a Hamiltonian that is Hermitian. It is shown that when the Hermiticity condition on the Hamiltonian is relaxed,…

Given any linear isometry from a Hilbert space to its square one can explicitly construct a so-called Pythagorean unitary representation of Richard Thompson's group F. We introduce a condition on the isometry implying that the associated…

Our main result is a theorem saying that a bounded operator $A$ on a Hilbert space belongs to a certain set associated with its self-commutator $[A^*,A]$, provided that $A-zI$ can be approximated by invertible operators for all complex…

Arveson's extension theorem asserts that B(H) is an injective object in the category of operator systems. Calling every self adjoint unital subspace of a unital *-algebra, a quasi operator system, we show that Arveson's theorem remains…

Let $A$ be a Banach algebra and $I$ a dense ideal in $A$. A natural question in the theory of operator algebras is whether the property that all derivations $D: A \to I$ are inner (implemented by elements in $I$) implies that all…

Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…

We consider the Wigner matrix $W_{n}$ of dimension $n \times n$ as $n \to \infty$. The objective of this paper is two folds: first we construct an operator $\mathcal{W}$ on a suitable Hilbert space $\mathcal{H}$ and then define a suitable…

Using a left multiplication defined on a right quaternionic Hilbert space, linear self-adjoint momentum operators on a right quaternionic Hilbert space are defined in complete analogy with their complex counterpart. With the aid of the…

The method of alternating projections involves orthogonally projecting an element of a Hilbert space onto a collection of closed subspaces. It is known that the resulting sequence always converges in norm if the projections are taken…

A very particular by-product of the result announced in the title reads as follows: Let $(X,<\cdot,\cdot>)$ be a real Hilbert space, $T:X\to X$ a compact and symmetric linear operator, and $z\in X$ such that the equation $T(x)-\|T\|x=z$ has…

Let $G$ be a locally compact abelian group with a Haar measure, and $Y$ be a measure space. Suppose that $H$ is a reproducing kernel Hilbert space of functions on $G\times Y$, such that $H$ is naturally embedded into $L^2(G\times Y)$ and is…

Let $\cK$ and $\cH$ be finite dimensional Hilbert spaces and let $\fP$ denote the cone of all positive linear maps acting from $\fB(\cK)$ into $\fB(\cH)$. We show that each map of the form $\phi(X)=AXA^*$ or $\phi(X)=AX^TA^*$ is an exposed…

In this paper we give a new and constructive approach to stationary scattering theory for pairs of self-adjoint operators $H_0$ and $H_1$ on a Hilbert space $\mathcal H$ which satisfy the following conditions: (i) for any open bounded…

The Heisenberg evolution of a given unitary operator corresponds classically to a fixed canonical transformation that is viewed through a moving coordinate system. The operators that form the bases of the Weyl representation and its Fourier…

Let $V$ be a vector space over a field $F$, $V^*$ its dual space and $L(V)$ the algebra of all linear operators on $V$. For an operator $a\in L(V)$ let $a*$ be its adjoint acting on $V*$, and for a subset $R$ of $L(V)$ let $R"$ be its…