Generalized -lattices of order ω+
T. Traczyk, W. Zarębski (1976)
Colloquium Mathematicae
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T. Traczyk, W. Zarębski (1976)
Colloquium Mathematicae
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Zhen-Yu Xiu, Xu Zheng (2024)
Kybernetika
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In this paper, on a bounded lattice , we give a new approach to construct uninorms via a given uninorm on the subinterval (or ) of under additional constraint conditions on and . This approach makes our methods generalize some known construction methods for uninorms in the literature. Meanwhile, some illustrative examples for the construction of uninorms on bounded lattices are provided.
Tiberiu Dumitrescu, Mihai Epure (2021)
Czechoslovak Mathematical Journal
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We study the multiplicative lattices which satisfy the condition for all . Call them sharp lattices. We prove that every totally ordered sharp lattice is isomorphic to the ideal lattice of a valuation domain with value group or . A sharp lattice localized at its maximal elements are totally ordered sharp lattices. The converse is true if has finite character.
W. Zarębski (1977)
Colloquium Mathematicae
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Scott Duke Kominers, Zachary Abel (2008)
Journal de Théorie des Nombres de Bordeaux
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We show that if is an extremal even unimodular lattice of rank with , then is generated by its vectors of norms and . Our result is an extension of Ozeki’s result for the case .
Abderrahman Retbi (2024)
Mathematica Bohemica
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We introduce and study the disjoint weak -convergent operators in Banach lattices, and we give a characterization of it in terms of sequences in the positive cones. As an application, we derive the domination and the duality properties of the class of positive disjoint weak -convergent operators. Next, we examine the relationship between disjoint weak -convergent operators and disjoint -convergent operators. Finally, we characterize order bounded disjoint weak -convergent operators...
Wolfgang Rump (2001)
Colloquium Mathematicae
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We extend our module-theoretic approach to Zavadskiĭ’s differentiation techniques in representation theory. Let R be a complete discrete valuation domain with quotient field K, and Λ an R-order in a finite-dimensional K-algebra. For a hereditary monomorphism u: P ↪ I of Λ-lattices we have an equivalence of quotient categories which generalizes Zavadskiĭ’s algorithms for posets and tiled orders, and Simson’s reduction algorithm for vector space categories. In this article we replace...
Gül Deniz Çaylı (2019)
Kybernetika
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In this study, we introduce new methods for constructing t-norms and t-conorms on a bounded lattice based on a priori given t-norm acting on and t-conorm acting on for an arbitrary element . We provide an illustrative example to show that our construction methods differ from the known approaches and investigate the relationship between them. Furthermore, these methods are generalized by iteration to an ordinal sum construction for t-norms and t-conorms on a bounded lattice. ...
Ioana Ghenciu (2023)
Commentationes Mathematicae Universitatis Carolinae
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We introduce the definition of -limited completely continuous operators, . The question of whether a space of operators has the property that every -limited subset is relative compact when the dual of the domain and the codomain have this property is studied using -limited completely continuous evaluation operators.
Elói Medina Galego (2011)
Colloquium Mathematicae
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We classify, up to isomorphism, the spaces of compact operators (E,F), where E and F are the Banach spaces of all continuous functions defined on the compact spaces , the topological products of Cantor cubes and intervals of ordinal numbers [0,α].
Kevin Esmeral, Osmin Ferrer, Jorge Jalk, Boris Lora Castro (2019)
Archivum Mathematicum
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In this paper the hyponormal operators on Krein spaces are introduced. We state conditions for the hyponormality of bounded operators focusing, in particular, on those operators for which there exists a fundamental decomposition of the Krein space with and invariant under .
Ioana Ghenciu, Paul Lewis (2008)
Bulletin of the Polish Academy of Sciences. Mathematics
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Results of Emmanuele and Drewnowski are used to study the containment of c₀ in the space , as well as the complementation of the space of w*-w compact operators in the space of w*-w operators from X* to Y.
Tathagata Basak (2014)
Journal de Théorie des Nombres de Bordeaux
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Using the geometry of the projective plane over the finite field , we construct a Hermitian Lorentzian lattice of dimension defined over a certain number ring that depends on . We show that infinitely many of these lattices are -modular, that is, , where is some prime in such that . The Lorentzian lattices sometimes lead to construction of interesting positive definite lattices. In particular, if is a rational prime such that is norm of some element in...
Antonio S. Granero, Marcos Sánchez (2008)
Banach Center Publications
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If X is a Banach space and C ⊂ X a convex subset, for x** ∈ X** and A ⊂ X** let d(x**,C) = inf||x**-x||: x ∈ C be the distance from x** to C and d̂(A,C) = supd(a,C): a ∈ A. Among other things, we prove that if X is an order-continuous Banach lattice and K is a w*-compact subset of X** we have: (i) and, if K ∩ X is w*-dense in K, then ; (ii) if X fails to have a copy of ℓ₁(ℵ₁), then ; (iii) if X has a 1-symmetric basis, then .
Songqing Chen, Huoxiong Wu, Qingying Xue (2014)
Studia Mathematica
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This paper is devoted to investigating the properties of multilinear conditions and conditions, which are suitable for the study of multilinear operators on Lebesgue spaces. Some monotonicity properties of and classes with respect to P⃗ and q are given, although these classes are not in general monotone with respect to the natural partial order. Equivalent characterizations of multilinear classes in terms of the linear classes are established. These results essentially improve...
Gül Deniz Çaylı, Funda Karaçal (2017)
Kybernetika
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In this paper, we propose the general methods, yielding uninorms on the bounded lattice , with some additional constraints on for a fixed neutral element based on underlying an arbitrary triangular norm on and an arbitrary triangular conorm on . And, some illustrative examples are added for clarity.