Kafes Normlu Riesz Cebirleri Üzerindeki Operatörler İçin Hahn-Banach Teoremi

Abstract

X ve E Riesz cebirleri ve p:X →E_+ monoton bir vektör normu olsun. Böylece (X,p,E) üçlüsü kafes normlu Riesz cebiri olarak adlandırılır. Bu çalışmada, Hahn-Banach teoreminin kafes normlu Riesz cebirlerindeki operatörler için genişletilmesini vereceğiz. Fakat bu çalışmadaki genişleme diğer Hahn-Banach teoremlerinden farlı olmaktadır. Ayrıca bu genişlemenin bazı sonuçlarının olduğunu göstermeketeyiz.

Keywords

• Hahn-Banach theoremi,Kafes normlu uzaylar,Riesz cebirleri,Riesz uzayı

Hahn-Banach Theorem for Operators on Lattice Normed Riesz Algebras

Abstract

Let X and E be Riesz algebras and p:X →E_+ be a monotone vector norm. Then the triple (X,p,E) is called lattice normed Riesz algebra. In this paper, we prove a generalization of the extension of the Hahn-Banach theorem for operators on the lattice normed Riesz algebras, in which the extension of one-step of that is not similar to the other Hahn-Banach theorems. In addition, we give some applications and results.

Keywords

• Hahn-Banach theorem,Lattice normed space,Riesz algebra,Riesz apaces

References

1. Aliprantis C.D., Burkinshaw O. Positive operators. Springer, Dordrecht, xx-376, 2006.
2. Aydın A. Multiplicative order convergence in f-algebras. Hacettepe Journal of Mathematics and Statistics, 49 998-1005, 2020.
3. Aydın A. The statistically unbounded τ-convergence on locally solid Riesz spaces. Turkish Journal of Mathematics, 44 949-956, 2020.
4. Bukhvalov A.V., Gutman A.E., Korotkov V.B., Kusraev A.G., Kutateladze S.S., Makarov B.M. Vector lattices and integral operators. Mathematics and its Applications, Kluwer Academic Publishers Group, Dordrecht, x-462, 1996.
5. Ercan Z., Wickstead A.W. Towards a theory of nonlinear orthomorphisms, In: Abramovich Y., Avgerinos E. and Yannelis N.C. (eds), Functional Analysis and Economic Theory, Springer, Berlin, 65-78, 1998.
6. Huijsmans C.B. Lattice-ordered algebras and f-algebras: a survey. Positive operators, Riesz spaces and economics, Springer, Berlin, 151-169, 1991.
7. Kusraev A.G. Dominated operators. Kluwer, Dordrecht, 141-186, 2000.
8. Luxemburg W.A.J., Zaanen A.C. Riesz spaces I. Amsterdam, The Netherlands: North-Holland Publishing Company, 1-514, 1971.

9. Pagter B.D. f-Algebras and orthomorphism. The Degree of Doctor of Philosophy, Leiden University, 1-149, 1981.
10. Turan B., Bilici F. The Hahn-Banach theorem for A-linear operators, Turkish Journal of Mathematics, 41 1360-1364, 2017.
11. Vincent G., Smith G. The Hahn-Banach theorem for modules. Proceedings of the London Mathematical Society, 17 72-90, 1967.
12. Zaanen A.C. Riesz spaces II. Amsterdam, The Netherlands: North-Holland Publishing Co., 1-720, 1983.