Continuous maximal regularity and analytic semigroups

TL;DR

This paper proves that continuous maximal regularity of a closed operator between Banach spaces guarantees it generates an analytic semigroup, linking regularity properties to semigroup generation in functional analysis.

Contribution

It establishes a direct connection between continuous maximal regularity and the generation of analytic semigroups for operators on Banach spaces.

Findings

Continuous maximal regularity implies generation of an analytic semigroup.

The operator's domain coincides with the space where the semigroup acts.

Provides a theoretical foundation linking regularity and semigroup theory.

Abstract

In this paper we establish a result regarding the connection between continuous maximal regularity and generation of analytic semigroups on a pair of densely embedded Banach spaces. More precisely, we show that continuous maximal regularity for a closed operator $A: E_1 \rightarrow E_0$ implies that $A$ generates a strongly continuous analytic semigroup on $E_0$ with domain equal $E_1$.