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Kafes Normlu Riesz Cebirleri Üzerindeki Operatörler İçin Hahn-Banach Teoremi

Year 2020, Volume: 8 Issue: 1, 737 - 741, 01.06.2020

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.

References

  • Aliprantis C.D., Burkinshaw O. Positive operators. Springer, Dordrecht, xx-376, 2006.
  • Aydın A. Multiplicative order convergence in f-algebras. Hacettepe Journal of Mathematics and Statistics, 49 998-1005, 2020.
  • Aydın A. The statistically unbounded τ-convergence on locally solid Riesz spaces. Turkish Journal of Mathematics, 44 949-956, 2020.
  • 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.
  • 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.
  • Huijsmans C.B. Lattice-ordered algebras and f-algebras: a survey. Positive operators, Riesz spaces and economics, Springer, Berlin, 151-169, 1991.
  • Kusraev A.G. Dominated operators. Kluwer, Dordrecht, 141-186, 2000.
  • Luxemburg W.A.J., Zaanen A.C. Riesz spaces I. Amsterdam, The Netherlands: North-Holland Publishing Company, 1-514, 1971.
  • Pagter B.D. f-Algebras and orthomorphism. The Degree of Doctor of Philosophy, Leiden University, 1-149, 1981.
  • Turan B., Bilici F. The Hahn-Banach theorem for A-linear operators, Turkish Journal of Mathematics, 41 1360-1364, 2017.
  • Vincent G., Smith G. The Hahn-Banach theorem for modules. Proceedings of the London Mathematical Society, 17 72-90, 1967.
  • Zaanen A.C. Riesz spaces II. Amsterdam, The Netherlands: North-Holland Publishing Co., 1-720, 1983.

Hahn-Banach Theorem for Operators on Lattice Normed Riesz Algebras

Year 2020, Volume: 8 Issue: 1, 737 - 741, 01.06.2020

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.

References

  • Aliprantis C.D., Burkinshaw O. Positive operators. Springer, Dordrecht, xx-376, 2006.
  • Aydın A. Multiplicative order convergence in f-algebras. Hacettepe Journal of Mathematics and Statistics, 49 998-1005, 2020.
  • Aydın A. The statistically unbounded τ-convergence on locally solid Riesz spaces. Turkish Journal of Mathematics, 44 949-956, 2020.
  • 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.
  • 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.
  • Huijsmans C.B. Lattice-ordered algebras and f-algebras: a survey. Positive operators, Riesz spaces and economics, Springer, Berlin, 151-169, 1991.
  • Kusraev A.G. Dominated operators. Kluwer, Dordrecht, 141-186, 2000.
  • Luxemburg W.A.J., Zaanen A.C. Riesz spaces I. Amsterdam, The Netherlands: North-Holland Publishing Company, 1-514, 1971.
  • Pagter B.D. f-Algebras and orthomorphism. The Degree of Doctor of Philosophy, Leiden University, 1-149, 1981.
  • Turan B., Bilici F. The Hahn-Banach theorem for A-linear operators, Turkish Journal of Mathematics, 41 1360-1364, 2017.
  • Vincent G., Smith G. The Hahn-Banach theorem for modules. Proceedings of the London Mathematical Society, 17 72-90, 1967.
  • Zaanen A.C. Riesz spaces II. Amsterdam, The Netherlands: North-Holland Publishing Co., 1-720, 1983.
There are 12 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Abdullah Aydın 0000-0002-0769-5752

Publication Date June 1, 2020
Published in Issue Year 2020 Volume: 8 Issue: 1

Cite

APA Aydın, A. (2020). Hahn-Banach Theorem for Operators on Lattice Normed Riesz Algebras. Muş Alparslan Üniversitesi Fen Bilimleri Dergisi, 8(1), 737-741.
AMA Aydın A. Hahn-Banach Theorem for Operators on Lattice Normed Riesz Algebras. MAUN Fen Bil. Dergi. June 2020;8(1):737-741.
Chicago Aydın, Abdullah. “Hahn-Banach Theorem for Operators on Lattice Normed Riesz Algebras”. Muş Alparslan Üniversitesi Fen Bilimleri Dergisi 8, no. 1 (June 2020): 737-41.
EndNote Aydın A (June 1, 2020) Hahn-Banach Theorem for Operators on Lattice Normed Riesz Algebras. Muş Alparslan Üniversitesi Fen Bilimleri Dergisi 8 1 737–741.
IEEE A. Aydın, “Hahn-Banach Theorem for Operators on Lattice Normed Riesz Algebras”, MAUN Fen Bil. Dergi., vol. 8, no. 1, pp. 737–741, 2020.
ISNAD Aydın, Abdullah. “Hahn-Banach Theorem for Operators on Lattice Normed Riesz Algebras”. Muş Alparslan Üniversitesi Fen Bilimleri Dergisi 8/1 (June 2020), 737-741.
JAMA Aydın A. Hahn-Banach Theorem for Operators on Lattice Normed Riesz Algebras. MAUN Fen Bil. Dergi. 2020;8:737–741.
MLA Aydın, Abdullah. “Hahn-Banach Theorem for Operators on Lattice Normed Riesz Algebras”. Muş Alparslan Üniversitesi Fen Bilimleri Dergisi, vol. 8, no. 1, 2020, pp. 737-41.
Vancouver Aydın A. Hahn-Banach Theorem for Operators on Lattice Normed Riesz Algebras. MAUN Fen Bil. Dergi. 2020;8(1):737-41.