Results 261 to 270 of about 1,358,389 (305)
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Canadian Journal of Mathematics, 1968
This note presents a useful explicit characterization of the free vector lattice FVL(ℵ) on ℵ generators as a vector lattice of piecewise linear, continuous functions on Rℵ, where ℵ is any cardinal and R is the set of real numbers. A transfinite construction of FVL(ℵ) has been given by Weinberg (14) and simplified by Holland (13, § 5).
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This note presents a useful explicit characterization of the free vector lattice FVL(ℵ) on ℵ generators as a vector lattice of piecewise linear, continuous functions on Rℵ, where ℵ is any cardinal and R is the set of real numbers. A transfinite construction of FVL(ℵ) has been given by Weinberg (14) and simplified by Holland (13, § 5).
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Multiplication in Vector Lattices
Canadian Journal of Mathematics, 1968B. Z. Vulih has shown (13) how an essentially unique intrinsic multiplication can be defined in a Dedekind complete vector lattice L having a weak order unit. Since this work is available only in Russian, a brief outline is given in § 2 (cf. also the review by E. Hewitt (4), and for details, consult (13) or (11)).
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Unbounded p-Convergence in Lattice-Normed Vector Lattices [PDF]
Siberian Advances in Mathematics, 2019 A net $x_α$ in a lattice-normed vector lattice $(X,p,E)$ is unbounded $p$-convergent to $x\in X$ if $p(|x_α-x|\wedge u)\xrightarrow{o} 0$ for every $u\in X_+$. This convergence has been investigated recently for $(X,p,E)=(X,\lvert\cdot \rvert,X)$ under the name of $uo$-convergence, for $(X,p,E)=(X,\lVert\cdot\rVert,{\mathbb R})$ under the name of $un ...
Eduard Emelyanov
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Multiband Vector Lattice Solitons
Physical Review Letters, 2003We predict multiband vector solitons in nonlinear periodic systems, using photonic lattices as a prime example. The solitons consist of two optical fields arising from different bands of the transmission spectrum, which involve both bound state and radiation mode components.
Oren, Cohen +4 more
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Approximating shortest lattice vectors is not harder than approximating closest lattice vectors
Information Processing Letters, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Oded Goldreich 0001 +3 more
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Contact Vectors of Point Lattices
Mathematical Notes, 2023The contact vectors of a lattice \(L\) are vectors \(l\) which are minimal in the \(l^{2}\)-norm in their parity class. In this paper, the author shows that, in the space of all symmetric matrices, the set of all contact vectors of the lattice \(L\) defines the subspace \(M(L)\) containing the Gram matrix \(A\) of the lattice \(L\).
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Vector Lattices Associated with Ordered Vector Spaces
Mediterranean Journal of Mathematics, 2010The vector lattice generated by a real Archimedean vector space \(V\) is considered. It is proved that the cone \(C\) of all positive linear forms on \(V\) separates elements of \(V\). Then the positive linear forms are determined in terms of conical measures on the cone \(C\).
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Prime Ideals in Vector Lattices
Canadian Journal of Mathematics, 1962Projectors, spectral functions, carriers, and collections of these objects are some of the tools which have been used to study vector lattices. One of our objectives in this paper is to show that these various approaches are not essentially different. We do this by proving that each of the above-mentioned objects can be identified with a collection of ...
Johnson, D. G., Kist, J. E.
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Girsanov’s theorem in vector lattices
Positivity, 2019The authors formulate and prove Girsanov's theorem in vector lattices. The methodology involves the theory of cross-variation processes, specifically the Kunita-Watanabe inequality, exponential processes, Itô's rule for multi-dimensional processes, and the integration by parts formula for martingales.
Grobler, Jacobus J. +1 more
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2018
The first of two results is a 1-1-correspondence between isomorphism classes of finite-dimensional vector lattices and finite rooted unlabelled trees. Thus the problem of counting isomorphism classes of finite-dimensional vector lattices reduces to the well-known combinatorial problem of counting these trees.
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The first of two results is a 1-1-correspondence between isomorphism classes of finite-dimensional vector lattices and finite rooted unlabelled trees. Thus the problem of counting isomorphism classes of finite-dimensional vector lattices reduces to the well-known combinatorial problem of counting these trees.
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