On greedy approximation in complex Banach spaces

TL;DR

This paper extends known results on greedy approximation algorithms from real Banach spaces to complex Banach spaces, broadening the theoretical understanding of these methods.

Contribution

It generalizes existing results for various greedy algorithms, beyond WCGA, to the setting of complex Banach spaces.

Findings

Extension of greedy approximation results to complex Banach spaces

Generalization of known algorithms beyond WCGA

Broader applicability of greedy methods in complex spaces

Abstract

The general theory of greedy approximation with respect to arbitrary dictionaries is well developed in the case of real Banach spaces. Recently, some of results proved for the Weak Chebyshev Greedy Algorithm (WCGA) in the case of real Banach spaces were extended to the case of complex Banach spaces. In this paper we extend some of known in the real case results for other than WCGA greedy algorithms to the case of complex Banach spaces.