Factorization in the Space of Henstock-Kurzweil Integrable Functions

M. Guadalupe Morales, Juan H. Arredondo

Abstract


In this work we extend the factorization theorem of Rudin and Cohen to HK(R), the space of Henstock-Kurzweil integrable functions. This implies a factorization for the isometric spaces AC and BC. We also study in this context the Banach algebra of functions HK(R) \cap BV(R), which is also a dense subspace of L2(R). In some sense this subspace is analogous to L1(R) \cap L2(R). However, while L1(R) \cap L2(R) factorizes as L1(R) L2(R) * L1(R), via the convolution operation *, it is shown in the paper that HK(R) \cap BV(R) * L1(R) is a Banach subalgebra of HK(R)\cap BV(R).

Keywords


Factorization, Banach algebla, Henstock-Kurzweil integral, bounded variation function

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