Displaying similar documents to “Regular vector lattices of continuous functions and Korovkin-type theorems-Part II”

On M-operators of q-lattices

Radomír Halaš (2002)

Discussiones Mathematicae - General Algebra and Applications

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It is well known that every complete lattice can be considered as a complete lattice of closed sets with respect to appropriate closure operator. The theory of q-lattices as a natural generalization of lattices gives rise to a question whether a similar statement is true in the case of q-lattices. In the paper the so-called M-operators are introduced and it is shown that complete q-lattices are q-lattices of closed sets with respect to M-operators.

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

Francesco Altomare, Mirella Cappelletti Montano (2005)

Studia Mathematica

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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...

Inverses and regularity of disjointness preserving operators

Y. A. Abramovich, A. K. Kitover

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A linear operator T: X → Y between vector lattices is said to be disjointness preserving if T sends disjoint elements in X to disjoint elements in Y. Two closely related questions are discussed in this paper: (1) If T is invertible, under what assumptions does the inverse operator also preserve disjointness? (2) Under what assumptions is the operator T regular? These problems were considered by the authors in [5] but the current paper (closely related to [5] but self-contained) reflects...

Narrow operators (a survey)

Mikhail Popov (2011)

Banach Center Publications

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Narrow operators are those operators defined on function spaces which are "small" at signs, i.e., at {-1,0,1}-valued functions. We summarize here some results and problems on them. One of the most interesting things is that if E has an unconditional basis then each operator on E is a sum of two narrow operators, while the sum of two narrow operators on L₁ is narrow. Recently this notion was generalized to vector lattices. This generalization explained the phenomena of sums: the set of...

Lattices with real numbers as additive operators

W. Holsztyński

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CONTENTSIntroduction............................... 5Paragraph 1............................... 6Paragraph 2............................... 13Paragraph 3............................... 21Paragraph 4............................... 27Paragraph 5............................... 36Paragraph 6............................... 42Paragraph 7............................... 52Paragraph 8............................... 60Paragraph 9............................... 70References....................................

Hypersubstitutions in orthomodular lattices

Ivan Chajda, Helmut Länger (2001)

Discussiones Mathematicae - General Algebra and Applications

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It is shown that in the variety of orthomodular lattices every hypersubstitution respecting all absorption laws either leaves the lattice operations unchanged or interchanges join and meet. Further, in a variety of lattices with an involutory antiautomorphism a semigroup generated by three involutory hypersubstitutions is described.

Proximities compatible with a given topology

Terrence E. Dooher, W. J. Thron

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CONTENTSI. Introduction............................................................................................................................................... 5II. Abstract lattices...................................................................................................................................... 7III. Completely regular lattices................................................................................................................. 9IV. Alternate characterizations...