Displaying similar documents to “О модифицированных классах p -ядерных, p -суммирующих и p -интегральных операторов.”

Sufficient conditions for a T-partial order obtained from triangular norms to be a lattice

Lifeng Li, Jianke Zhang, Chang Zhou (2019)

Kybernetika

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For a t-norm T on a bounded lattice ( L , ) , a partial order T was recently defined and studied. In [11], it was pointed out that the binary relation T is a partial order on L , but ( L , T ) may not be a lattice in general. In this paper, several sufficient conditions under which ( L , T ) is a lattice are given, as an answer to an open problem posed by the authors of [11]. Furthermore, some examples of t-norms on L such that ( L , T ) is a lattice are presented.

2-summing multiplication operators

Dumitru Popa (2013)

Studia Mathematica

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Let 1 ≤ p < ∞, = ( X ) n be a sequence of Banach spaces and l p ( ) the coresponding vector valued sequence space. Let = ( X ) n , = ( Y ) n be two sequences of Banach spaces, = ( V ) n , Vₙ: Xₙ → Yₙ, a sequence of bounded linear operators and 1 ≤ p,q < ∞. We define the multiplication operator M : l p ( ) l q ( ) by M ( ( x ) n ) : = ( V ( x ) ) n . We give necessary and sufficient conditions for M to be 2-summing when (p,q) is one of the couples (1,2), (2,1), (2,2), (1,1), (p,1), (p,2), (2,p), (1,p), (p,q); in the last case 1 < p < 2, 1 < q < ∞. ...

Construction of uninorms on bounded lattices

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 ( L , , 0 , 1 ) , with some additional constraints on e L { 0 , 1 } for a fixed neutral element e L { 0 , 1 } based on underlying an arbitrary triangular norm T e on [ 0 , e ] and an arbitrary triangular conorm S e on [ e , 1 ] . And, some illustrative examples are added for clarity.

Explicit construction of normal lattice configurations

Mordechay B. Levin, Meir Smorodinsky (2005)

Colloquium Mathematicae

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We extend Champernowne’s construction of normal numbers to base b to the d case and obtain an explicit construction of a generic point of the d shift transformation of the set 0 , 1 , . . . , b - 1 d .

Duality of measures of non-𝒜-compactness

Juan Manuel Delgado, Cándido Piñeiro (2015)

Studia Mathematica

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Let be a Banach operator ideal. Based on the notion of -compactness in a Banach space due to Carl and Stephani, we deal with the notion of measure of non–compactness of an operator. We consider a map χ (respectively, n ) acting on the operators of the surjective (respectively, injective) hull of such that χ ( T ) = 0 (respectively, n ( T ) = 0 ) if and only if the operator T is -compact (respectively, injectively -compact). Under certain conditions on the ideal , we prove an equivalence inequality involving...

Orthogonality and complementation in the lattice of subspaces of a finite vector space

Ivan Chajda, Helmut Länger (2022)

Mathematica Bohemica

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We investigate the lattice 𝐋 ( 𝐕 ) of subspaces of an m -dimensional vector space 𝐕 over a finite field GF ( q ) with a prime power q = p n together with the unary operation of orthogonality. It is well-known that this lattice is modular and that the orthogonality is an antitone involution. The lattice 𝐋 ( 𝐕 ) satisfies the chain condition and we determine the number of covers of its elements, especially the number of its atoms. We characterize when orthogonality is a complementation and hence when 𝐋 ( 𝐕 ) is orthomodular....

Some methods to obtain t-norms and t-conorms on bounded lattices

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 L based on a priori given t-norm acting on [ a , 1 ] and t-conorm acting on [ 0 , a ] for an arbitrary element a L { 0 , 1 } . 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. ...

On C * -spaces

P. Srivastava, K. K. Azad (1981)

Matematički Vesnik

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