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Compactness properties of weighted summation operators on trees

Mikhail Lifshits, Werner Linde (2011)

Studia Mathematica

We investigate compactness properties of weighted summation operators V α , σ as mappings from ℓ₁(T) into ℓ q ( T ) for some q ∈ (1,∞). Those operators are defined by ( V α , σ x ) ( t ) : = α ( t ) ∑ s ⪰ t σ ( s ) x ( s ) , t ∈ T, where T is a tree with partial order ⪯. Here α and σ are given weights on T. We introduce a metric d on T such that compactness properties of (T,d) imply two-sided estimates for e ₙ ( V α , σ ) , the (dyadic) entropy numbers of V α , σ . The results are applied to concrete trees, e.g. moderately increasing, biased or binary trees and to weights with α(t)σ(t)...

Complemented ordered sets

Ivan Chajda (1992)

Archivum Mathematicum

We introduce the concept of complementary elements in ordered sets. If an ordered set S is a lattice, this concept coincides with that for lattices. The connections between distributivity and the uniqueness of complements are shown and it is also shown that modular complemented ordered sets represents “geometries” which are more general than projective planes.

Congruence classes in Brouwerian semilattices

Ivan Chajda, Helmut Länger (2001)

Discussiones Mathematicae - General Algebra and Applications

Brouwerian semilattices are meet-semilattices with 1 in which every element a has a relative pseudocomplement with respect to every element b, i. e. a greatest element c with a∧c ≤ b. Properties of classes of reflexive and compatible binary relations, especially of congruences of such algebras are described and an abstract characterization of congruence classes via ideals is obtained.

Congruence kernels of distributive PJP-semilattices

S. N. Begum, Abu Saleh Abdun Noor (2011)

Mathematica Bohemica

A meet semilattice with a partial join operation satisfying certain axioms is a JP-semilattice. A PJP-semilattice is a pseudocomplemented JP-semilattice. In this paper we describe the smallest PJP-congruence containing a kernel ideal as a class. Also we describe the largest PJP-congruence containing a filter as a class. Then we give several characterizations of congruence kernels and cokernels for distributive PJP-semilattices.

Congruences in ordered sets

Ivan Chajda, Václav Snášel (1998)

Mathematica Bohemica

A concept of congruence preserving upper and lower bounds in a poset P is introduced. If P is a lattice, this concept coincides with the notion of lattice congruence.

Congruences in ordered sets and LU compatible equivalences

Václav Snášel, Marek Jukl (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

A concept of equivalence preserving upper and lower bounds in a poset P is introduced. If P is a lattice, this concept coincides with the notion of lattice congruence.

Currently displaying 181 – 200 of 995