On explicit constructions of auerbach bases in separable Banach spaces

TL;DR

This paper provides explicit methods for constructing Auerbach bases in certain separable Banach spaces, addressing a question about their existence in specific subspaces and function spaces.

Contribution

It offers explicit constructions of Auerbach bases in subspaces of c0 with finite codimension and in C(K) spaces for countable compact metric spaces.

Findings

Constructed Auerbach bases in subspaces of c0 with finite codimension.

Established existence of Auerbach bases in C(K) spaces for countable compact metric K.

Answered a question posed by A. Pelczynski regarding these bases.

Abstract

This paper considers explicit constructions of Auerbach bases in separable Banach spaces. Answering the question of A. Pe{\l}czy{\'n}ski, we prove by construction the existence of Auerbach basis in arbitrary subspace of $c_0$ of finite codimension and in the space $C(K)$ for $K$ compact countable metric space.