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Products in almost f -algebras

Karim Boulabiar (2000)

Commentationes Mathematicae Universitatis Carolinae

Let A be a uniformly complete almost f -algebra and a natural number p ∈ { 3 , 4 , ⋯ } . Then Π p ( A ) = { a 1 ⋯ a p ; a k ∈ A , k = 1 , ⋯ , p } is a uniformly complete semiprime f -algebra under the ordering and multiplication inherited from A with Σ p ( A ) = { a p ; 0 ≤ a ∈ A } as positive cone.

Regular vector lattices of continuous functions and Korovkin-type theorems-Part I

Francesco Altomare, Mirella Cappelletti Montano (2005)

Studia Mathematica

We introduce and study a new class of locally convex vector lattices of continuous functions on a locally compact Hausdorff space, which we call regular vector lattices. We investigate some general properties of these spaces and of the subspaces of so-called generalized affine functions. Moreover, we present some Korovkin-type theorems for continuous positive linear operators; in particular, we study Korovkin subspaces for finitely defined operators, for the identity operator and for positive...

Representation theorem for convex effect algebras

Stanley P. Gudder, Sylvia Pulmannová (1998)

Commentationes Mathematicae Universitatis Carolinae

Effect algebras have important applications in the foundations of quantum mechanics and in fuzzy probability theory. An effect algebra that possesses a convex structure is called a convex effect algebra. Our main result shows that any convex effect algebra admits a representation as a generating initial interval of an ordered linear space. This result is analogous to a classical representation theorem for convex structures due to M.H. Stone.

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