On explicit constructions of auerbach bases in separable Banach spaces
Robert Bogucki

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 of finite codimension and in the space for compact countable metric space.
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Taxonomy
TopicsAdvanced Banach Space Theory · Advanced Operator Algebra Research · Holomorphic and Operator Theory
