Strengthened fixed point property and products in ordered sets
Josef Niederle (2007)
Mathematica Slovaca
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Josef Niederle (2007)
Mathematica Slovaca
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Vítězslav Novák (1965)
Czechoslovak Mathematical Journal
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Shengzhao Hou, Shuyun Wei (2008)
Studia Mathematica
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Let f, g be in the analytic function ring Hol(𝔻) over the unit disk 𝔻. We say that f ⪯ g if there exist M > 0 and 0 < r < 1 such that |f(z)| ≤ M|g(z)| whenever r < |z| < 1. Let X be a Hilbert space contained in Hol(𝔻). Then X is called an ordered Hilbert space if f ⪯ g and g ∈ X imply f ∈ X. In this note, we mainly study the connection between an ordered analytic Hilbert space and its reproducing kernel. We also consider when an invariant subspace of the whole space...
V. Novák (1964)
Fundamenta Mathematicae
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Vítězslav Novák, Miroslav Novotný (1987)
Czechoslovak Mathematical Journal
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Radomír Halaš, Daniel Hort (2003)
Czechoslovak Mathematical Journal
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We characterize totally ordered sets within the class of all ordered sets containing at least four-element chains. We use a simple relationship between their isotone transformations and the so called 1-endomorphism which is introduced in the paper. Later we describe 1-, 2-, 3-, 4-homomorphisms of ordered sets in the language of super strong mappings.
Kent, Darrell C., Richmond, T.A. (1990)
International Journal of Mathematics and Mathematical Sciences
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