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

Note on "construction of uninorms on bounded lattices"

Xiu-Juan Hua, Hua-Peng Zhang, Yao Ouyang (2021)

Kybernetika

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In this note, we point out that Theorem 3.1 as well as Theorem 3.5 in G. D. Çaylı and F. Karaçal (Kybernetika 53 (2017), 394-417) contains a superfluous condition. We have also generalized them by using closure (interior, resp.) operators.

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...

A characterization of uninorms on bounded lattices via closure and interior operators

Gül Deniz Çayli (2023)

Kybernetika

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Uninorms on bounded lattices have been recently a remarkable field of inquiry. In the present study, we introduce two novel construction approaches for uninorms on bounded lattices with a neutral element, where some necessary and sufficient conditions are required. These constructions exploit a t-norm and a closure operator, or a t-conorm and an interior operator on a bounded lattice. Some illustrative examples are also included to help comprehend the newly added classes of uninorms. ...

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....................................

On the construction of t-norms (t-conorms) by using interior (closure) operator on bounded lattices

Emel Aşıcı (2022)

Kybernetika

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Recently, the topic of construction methods for triangular norms (triangular conorms), uninorms, nullnorms, etc. has been studied widely. In this paper, we propose construction methods for triangular norms (t-norms) and triangular conorms (t-conorms) on bounded lattices by using interior and closure operators, respectively. Thus, we obtain some proposed methods given by Ertuğrul, Karaçal, Mesiar [15] and Çaylı [8] as results. Also, we give some illustrative examples. Finally, we conclude...

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.