Search results for " Hilbert spaces"

Rigged Hilbert spaces and contractive families of Hilbert spaces

2013

The existence of a rigged Hilbert space whose extreme spaces are, respectively, the projective and the inductive limit of a directed contractive family of Hilbert spaces is investigated. It is proved that, when it exists, this rigged Hilbert space is the same as the canonical rigged Hilbert space associated to a family of closable operators in the central Hilbert space.

Bessel sequences, Riesz-like bases and operators in Triplets of Hilbert spaces

2016

Riesz-like bases for a triplet of Hilbert spaces are investigated, in connection with an analogous study for more general rigged Hilbert spaces performed in a previous paper. It is shown, in particular, that every \(\omega \)-independent, complete (total) Bessel sequence is a (strict) Riesz-like basis in a convenient triplet of Hilbert spaces. An application to non self-adjoint Schrodinger-type operators is considered. Moreover, some of the simplest operators we can define by them and their dual bases are studied.

On distinguished polynomials and their projections

2012

We study projections and injections between projective tensor products spaces or spaces of polynomials and we show that the example of a polynomial constructed in (4), that is neither p-dominated nor compact, can be identified with the projection map of the symmetric tensor product onto the space. Also we give a characterization of the weak and quasi approximation properties on symmetric tensor products.

On non-self-adjoint operators defined by Riesz bases in Hilbert and rigged Hilbert spaces

2018

In this paper we discuss some results on non self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that their eigenvectors form Riesz bases of a certain Hilbert space. Also, we exhibit a generalization of those results to the case of rigged Hilbert spaces, and we also consider the problem of the factorization of the aforementioned Hamiltonians in terms of generalized lowering and raising operators.

Operators in rigged Hilbert spaces: toward a spectral analysis

Some algebraic and topological properties of the nonabelian tensor product

2013

Several authors investigated the properties which are invariant under the passage from a group to its nonabelian tensor square. In the present note we study this problem from the viewpoint of the classes of groups and the methods allow us to prove a result of invariance for some geometric properties of discrete groups.

Intrinsic characterization of space‐time symmetric tensors

1992

This paper essentially deals with the classification of a symmetric tensor on a four‐dimensional Lorentzian space. A method is given to find the algebraic type of such a tensor. A system of concomitants of the tensor is constructed, which allows one to know the causal character of the eigenspace corresponding to a given eigenvalue, and to obtain covariantly their eigenvectors. Some algebraic as well as differential applications are considered.

Riesz-like bases in rigged Hilbert spaces

2015

The notions of Bessel sequence, Riesz-Fischer sequence and Riesz basis are generalized to a rigged Hilbert space $\D[t] \subset \H \subset \D^\times[t^\times]$. A Riesz-like basis, in particular, is obtained by considering a sequence $\{\xi_n\}\subset \D$ which is mapped by a one-to-one continuous operator $T:\D[t]\to\H[\|\cdot\|]$ into an orthonormal basis of the central Hilbert space $\H$ of the triplet. The operator $T$ is, in general, an unbounded operator in $\H$. If $T$ has a bounded inverse then the rigged Hilbert space is shown to be equivalent to a triplet of Hilbert spaces.