H\"Older type inequalities for orthosymmetric bilinear operators
Author: Kusraev Anatoly G.
Journal: Владикавказский математический журнал @vmj-ru
Article in issue: 3 т.9, 2007.
Free access
An interplay between squares of vector lattice and homogeneous functional calculus is considered and H\"older type inequalities for orthosymmetric bilinear operators are obtained.
Orthosymmetric bilinear operator, lattice bimorphism, homogeneous functional calculus, squares of vector lattices, h\"older type inequalities
Short address: https://sciup.org/14318219
IDR: 14318219 | UDC: 517.98
References H\"Older type inequalities for orthosymmetric bilinear operators
- Abramovich Y. A., Aliprantis C. D. An Invitation to Operator Theory//Amer. Math. Soc.-Rhode Island: Providence, 2002.-V. 50 (Graduate Studies in Mathematics).
- Aliprantis C. D., Burkinshaw O. Positive Operators.-New York: Acad. Press, 1985.-xvi+367 p.
- Aczel J., Dhombres J. Functional Equations in Several Variables.-Cambridge etc.: Cambridge Univ. Press, 1989.
- Bernau S. J., Huijsmans C. B. The Schwarz inequality in Archimedean f-algebras//Indag. Math. N. S.-1996.-V. 7, № 2.-P. 137-148.
- Bourbaki N. Integration. Ch. 1-8.-Paris: Hermann, 1967.-In French.
- Buskes G., de Pagter B., van Rooij A. Functional calculus in Riesz spaces//Indag. Math. N. S.-1991.-V. 4, № 2.-P. 423-436.
- Buskes G., Kusraev A. G. Representation and extension of orthoregular bilinear operators//Vladikavkaz Math. J.-2007.-V. 8, № 1.-P. 16-29.
- Buskes G., van Rooij A. Almost f-algebras: commutativity and the Cauchy-Schwarz inequality//Positivity.-2000.-V. 4.-P. 227-231.
- Buskes G., van Rooij A. Squares of Riesz spaces//Rocky Mountain J. Math.-2001.-V. 31, №. 1.-P. 45-56.
- Drnovsek R. Spectral inequalities for compact integral operators on Banach function spaces//Math. Proc. Camb. Phil. Soc.-1992.-V. 112.-P. 589-598.
- Drnovsek R., Peperko A. Inequalities for the Hadamard weighted geometric mean of positive kernel operators on Banach function spaces//Positivity.-2006.-V. 10, № 4.-P. 613-626.
- Haase M. Convexity inequalities for positive operators//Positivity.-2007.-V. 11, № 1.-P. 57-68.
- Krivine J. L. Theoremes de factorisation dans les espaces reticules//Seminar Maurey-Schwartz.-Paris: Ecole Politech, 1973/74.-Exp. 22/23.-22 p.
- Kusraev A. G. Dominated Operators.-Dordrecht: Kluwer, 2000.-445 p.
- Kusraev A. G. On the structure of orthosymmetric bilinear operators in vector lattices//Dokl. RAS.-2006.-V. 408, № 1.-P. 25-27.
- Kusraev A. G. Orthosymmetric Bilinear Operators.-Vladikavkaz: Inst. of Appl. Math. and Infomat. VSC RAS, 2007.
- Lindenstrauss J., Tzafriri L. Classical Banach Spaces. V. 2. Function Spaces.-Berlin etc.: Springer, 1979.-243 pp.
- Lozanovskiui G. Ya. On topologically reflexive KB-spaces//Dokl. Akad. Nauk SSSR.-1964.-V. 158, № 3.-P. 516-519.
- Lozanovskiui G. Ya. The functions of elements of vector lattices//Izv. Vyssh. Uchebn. Zaved. Mat.-1973.-№. 4.-P. 45-54.
- Rockafellar R. T. Convex Analysis.-Princeton-New Jersey: Princeton Univ. Press, 1970.-468 p.
- Schwarz H.-V. Banach Lattices and Operators.-Leipzig: Teubner, 1984.-208 pp.
- Szulga J. (p,r)-convex functions on vector lattices//Proc. Edinburg Math. Soc.-1994.-V. 37.-P. 207-226.