Related papers: A constructive presentation of rigged Hilbert spac…

We construct some separable infinite dimensional homogeneous Hilbertian operator spaces which generalize the row and column spaces R and C. We show that separable infinite-dimensional Hilbertian JC*-triples are completely isometric to an…

Let $H$ be a complex Hilbert space and let ${\mathcal P}(H)$ be the associated projective space (the set of rank-one projections). Suppose that $\dim H\ge 3$. We prove the following Wigner-type theorem: if $H$ is finite-dimensional, then…

A ladder structure of operators is presented for the associated Legendre polynomials and the spherical harmonics showing that both belong to the same irreducible representation of so(3,2). As both are also bases of square-integrable…

Given a complex, separable Hilbert space $\mathcal{H}$, we characterize those operators for which $\| P T (I-P) \| = \| (I-P) T P \|$ for all orthogonal projections $P$ on $\mathcal{H}$. When $\mathcal{H}$ is finite-dimensional, we also…

We use the plethystic exponential and the Molien-Weyl formula to compute the Hilbert series (generating funtions), which count gauge invariant operators in N=1 supersymmetric SU(N_c), Sp(N_c), SO(N_c) and G_2 gauge theories with 1 adjoint…

The Hardy space H^2(R) for the upper half plane together with a unimodular function group representation u(\lambda) = \exp(i(\lambda_1\psi_1 + ... + \lambda_n\psi_n)) for \lambda in R^n, gives rise to a manifold M of orthogonal projections…

Let $G$ be a discrete countable group, and let $\Gamma$ be an almost normal subgroup. In this paper we investigate the classification of (projective) unitary representations $\pi$ of $G$ into the unitary group of the Hilbert space…

We prove that for every semigroup of Schwarz maps on the von~Neumann algebra of all bounded linear operators on a Hilbert space which has a subinvariant faithful normal state there exists an associated semigroup of contractions on the space…

The image of a given orthonormal basis for a separable Hilbert space $\mathcal{H}$ under a bijective, bounded, and linear operator acting on $\mathcal{H}$ is called a Riesz basis of $\mathcal{H}$. Contrary to what happens with Riesz bases…

We introduce the notion of an orthocomplemented subspace of a Hilbert space H, that is, a pair of orthogonal closed subspaces of H, as a two-dimensional counterpart to the one-dimensional notion of a closed subspace of H. Orthocomplemented…

We study two extension problems, and their interconnections: (i) extension of positive definite (p.d.) continuous functions defined on subsets in locally compact groups $G$; and (ii) (in case of Lie groups $G$) representations of the…

The diagonal in a product of projective spaces is cut out by the ideal of 2x2-minors of a matrix of unknowns. The multigraded Hilbert scheme which classifies its degenerations has a unique Borel-fixed ideal. This Hilbert scheme is generally…

We associate to any Riemannian symmetric space (of finite or infinite dimension) a L$^*$-algebra, under the assumption that the curvature operator has a fixed sign. L$^*$-algebras are Lie algebras with a pleasant Hilbert space structure.…

Consider the Plancherel decomposition of the tensor product of a highest weight and a lowest weight unitary representations of $SL_2$. We construct explicitly the action of the Lie algebra $sl_2 + sl_2$ in the direct integral of Hilbert…

For a projective variety $X$ and a line bundle $L$ over $X$, one considers the $L-$twisted global differential operator algebra $\call{D}_L(X)$ which naturally operates on the space of global sections $H^0(X,L)$. In the case where $X$ is…

We prove that the operator Hilbert space OH does not embed completely isomorphically into the predual of a semi-finite von Neumann algebra. This complements Junge's recent result that it admits such an embedding in the non semi-finite case.

Motivated by the recent developments of pseudo-hermitian quantum mechanics, we analyze the structure of unbounded metric operators in a Hilbert space. It turns out that such operators generate a canonical lattice of Hilbert spaces, that is,…

We propose a new viewpoint on Hilbert scales extending them by means of all Hilbert spaces that are interpolation ones between spaces on the scale. We prove that this extension admits an explicit description with the help of…

This review paper contains a concise introduction to highest weight representations of infinite dimensional Lie algebras, vertex operator algebras and Hilbert schemes of points, together with their physical applications to elliptic genera…

It is proved that, in the Misra-Prigogine-Courbage Theory of Irreversibility using the Internal Time superoperator, fixing its associated non-unitary transformation $\Lambda$, amounts to rigging the corresponding Hilbert-Liouville space.…