Journal of Advances in Mathematics and Computer Science

On Natural Characterizations of Tensor Integrability

Mangatiana A. Robdera *

Department of Mathematics, University of Botswana, Private Bag 0022, Gaborone, Botswana.

*Author to whom correspondence should be addressed.

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Abstract

We revisit the definition of the tensor integrability introduced in [1], and prove some useful characterizations that provide a foundation for studying relevant properties to the integration theory. As applications, we obtain some representation theorems for the projective and injective tensor products of the space of scalar integrable functions with Banach spaces.

Keywords: Vector integral, tensor integral, tensor product

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