Rigged Hilbert spaces and inductive limits

TL;DR

This paper presents a simplified method for constructing a rigged Hilbert space using inductive limits of finite-dimensional subspaces, enhancing the understanding of the structure of nuclear spaces.

Contribution

It introduces a new approach to building rigged Hilbert spaces by leveraging inductive limits, simplifying previous complex constructions.

Findings

Constructed a nuclear space as an inductive limit of finite-dimensional subspaces.

Established the rigged Hilbert space structure with the constructed nuclear space.

Simplified the existing construction by Bellomonte and Trapani.

Abstract

We construct a nuclear space $\Phi$ as an inductive limit of finite-dimensional subspaces of a Hilbert space $H$ in such a way that $(\Phi,H,\Phi')$ becomes a rigged Hilbert space, thus simplifying the construction by Bellomonte and Trapani.