The tensor product of f-algebras

Abstract

In this paper we study the tensor product of two f -algebras. We show that the Riesz Subspace generated by a subalgebra in an f -algebra is an algebra in order to prove that the Riesz tensor product of two f -algebras has a structure of an f -algebra.

Tensor Products of f-algebras

“…There is overlap between our results and those obtained (for unital and semi-prime f -algebras, and using different methods) in [1].…”

Characterisation of conditional weak mixing via ergodicity of the tensor product in Riesz Spaces

“…For the general construction of the tensor product of Riesz spaces and f -algebras we refer the reader to [3,4,7,9,20,21]. We proceed here using the approaches of [3,7,9].…”

“…For the general construction of the tensor product of Riesz spaces and f -algebras we refer the reader to [3,4,7,9,20,21]. We proceed here using the approaches of [3,7,9]. As shown in [9], if E and F are Archimedean Riesz spaces then a partial ordering can be induced on E ⊗ F by the cone generated by E + ⊗ F + .…”