Arveson dichotomy and essential fractality

TL;DR

This paper explores the relationship between Arveson dichotomy and essential fractality, providing new proofs and restriction theorems to advance understanding in spectral approximation theory.

Contribution

It offers a new proof of the fractal restriction theorem, links essential fractality with Arveson dichotomy, and derives a restriction theorem for essential fractality.

Findings

New proof of the fractal restriction theorem

Established connection between essential fractality and Arveson dichotomy

Derived a restriction theorem for essential fractality

Abstract

The notions of fractal and essentially fractal algebras of approximation sequences and of the Arveson dichotomy have proved extremely useful for several spectral approximation problems. The purpose of this short note is threefold: to present a short new proof of the fractal restriction theorem, to relate essential fractality with Arveson dichotomy, and to derive a restriction theorem for essential fractality.