Homogeneous polynomials, root mean power, and geometric means in vector lattices

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system’s guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	Dear authors! Submission of all materials is carried out only electronically through Online Submission System in personal account. DOI: 10.23671/VNC.2014.4.10260 Homogeneous polynomials, root mean power, and geometric means in vector lattices Kusraeva, Z. A. Vladikavkaz Mathematical Journal 2014. Vol. 16. Issue 4. Abstract: It is proved that for a homogeneous orthogonally additive polynomial \(P\) of degree \(s\in\mathbb{N}\) from a uniformly complete vector lattice \(E\) to some convex bornological space the equations \(P(\mathfrak{S}_s(x_{1},\ldots,x_{N}))= P(x_{1})+\ldots+P(x_{N})\) and \(P(\mathfrak{G}(x_{1},\ldots,x_{s}))= \check{P}(x_{1},\ldots,x_{s})\) hold for all positive \(x_{1},\ldots,x_{s}\in E\), where \(\check{P}\) is an \(s\)-linear operator generating \(P\), while \(\mathfrak{S}_s(x_{1},\ldots,x_{N})\) and \(\mathfrak{G}(x_{1},\ldots,x_{s})\) stand respectively for root mean power and geometric mean in the sense of homogeneous functional calculus. Keywords: vector lattice, homogeneous polynomial, linearization of a polynomial, root mean power, geometric mean Language: Russian Download the full text For citation: Kusraeva Z. A. Homogeneous polynomials, root mean power, and geometric means in vector lattices // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 16, no. 4, pp. 49-53. DOI 10.23671/VNC.2014.4.10260 + References 1. Aliprantis C. D., Burkinshaw O. Positive Operators, N. Y., Acad. Press, 1985. xvi+367 p. 2. Benyamini Y., Lassalle S., Llavona J. G. Homogeneous orthogonally additive polynomials on Banach lattices. Bull. London Math. Soc., 2006, vol. 38, no. 3. pp. 459-469. 3. Boulabiar K., Buskes G. Vector lattice powers: f-algebras and functional Calculus. Comm. Algebra, 2006, vol. 34, no. 4, pp. 1435-1442. 4. Bu Q., Buskes G., Kusraev A. G. Bilinear maps on product of vector lattices: A survey. Positivity, Eds. K. Boulabiar, G. Buskes, A. Triki. Basel a.o., Birkhauser, 2007, pp. 97-126. 5. Buskes, G., de Pagter.B., van Rooij. A. Functional calculus on Riesz spaces. Indag. Math. (N.S.), 1991, vol. 4, no. 2, pp. 423-436. 6. Meyer-Nieberg P. Banach Lattices. Berlin etc., Springer, 1991, 395 p. 7. Kusraeva Z. A. Representation of orthogonally additive polynomials. Siberian Math. J., 2011, vol. 52, no. 2, pp. 248-255. ← Contents of issue


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