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On greedy approximation in complex Banach spaces

A. Gasnikov, V. Temlyakov

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.

On greedy approximation in complex Banach 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.
Paper Structure (6 sections, 14 theorems, 127 equations)

This paper contains 6 sections, 14 theorems, 127 equations.

Table of Contents

  1. Introduction
  2. Definitions and Lemmas
  3. Main results
  4. WGAFR
  5. GAWR
  6. Incremental Algorithm

Key Result

Lemma 2.1

Let $x\neq0$. Then

Theorems & Definitions (28)

  • Lemma 2.1
  • proof
  • Lemma 2.2
  • proof
  • Remark 2.1
  • proof
  • Lemma 2.3
  • proof
  • Lemma 2.4
  • proof
  • ...and 18 more