Operator Linear-2 Terbatas pada Ruang Bernorma-2 Non-Archimedean

  • Burhanudin Arif Nurnugroho Universitas Ahmad Dahlan
  • Supama Supama Universitas Gadjah Mada
  • A. Zulijanto Universitas Gadjah Mada
Keywords: norma, ruang operator, terbatas, linear-2, bernorma-2 non-Archimedean


Di dalam paper ini dikonstruksikan operator linear-2 terbatas dari X2 ke Y , dengan X  ruang bernorma-2 non-Archimedean dan  ruang bernorma non-Archimedean. Di dalam paper ini ditunjukan bahwa himpunan semua operator linear-2 terbatas dari X2 to Y , ditulis B(X2, Y) merupakan ruang bernorma non-Archimedean. Selanjutnya, ditunjukan bahwa B(X2, Y), apabila Y ruang Banach non-Archimedean.

[In this paper we construct  bounded 2-linear operators from X2  to Y, where X is non-Archimedean 2-normed spaces and  is a non-Archimedean-normed space. We prove that the set of all bounded 2-linear operators from X2 to Y  , denoted by B(X2, Y) is a non-Archimedean normed spaces. Furthermore, we show that B(X2, Y) is a non-Archimedean Banach normed space, whenever Y is a non-Archimedean Banach space.]


Download data is not yet available.

Author Biographies

Burhanudin Arif Nurnugroho, Universitas Ahmad Dahlan

Program Studi Pendididkan Matematika, Fakultas Keguruan dan Ilmu Pendidikan

Supama Supama, Universitas Gadjah Mada

Jurusan Matematika, Fakultas Matematika dan Ilmu Pengatahuan Alam

A. Zulijanto, Universitas Gadjah Mada

Jurusan Matematika, Fakultas Matematika dan Ilmu Pengatahuan Alam


S. Gahler. 1964. Lineare 2-normierte raume. Math. Nachr, 28: 1-43.
H. Gunawan and Mashadi. 2001. On n-Normed Spaces. Int. J. Math. Sci., 27: 631-639.
S.M. Gozali, H. Gunawan, and O. Neswan. 2010. On n-Norms and Bounded n-Linear Functionals in a Hilbert Spaces. Ann. Funct. Anali. 1: 72-79.
Agus L. Soenjaya. 2012. On n-Bounded and n-Continuous Operator in n-Normed Spaces. J. Indones. Math. Soc. Vol. 18, No. 1: 45-56.
Hahng-Yun Chu, Se-Hyun Ku, and Dong Seung Kang. 2008. Characterizations on 2-Isometries. Journal math. Anal. Appl. 340:641-628.
R. W. Freese, Y. J. Cho. 2001. Geometry of Linear 2-Normed Spaces. Hauppauge, New-York, Nova Science Publisher Inc.
A. F. Monna. 1943. Linear Functional Equations in Non-Archimedean Banach Spaces. Nederl. Akad. Wetensch. Verslagen. Afd. Natuurkunde, 52: 654-661.
C. Perez-Garcia and W. H. Schikhof. 2010. Locally Convex Spaces Over Non-Archimedean Valued Fields. Cambridge, Cambridge University Press.
Toka Diagana. 2009. Non-Archimedean Linear Operators and Applications. New York, Nova Science Publisher Inc.
M. Amyari and Gh. Sadeghi. 2009. Mapping on Non-Archimedean Strictly 2-Convex 2-Normed Spaces. The 〖18〗^th Seminar on Mathematical Analysis and its Applications, Tarbiat Moallem University: 57-60.
Jaeyoo Choy and Se-Hyun Ku. 2009. Characterization on 2-isometries in Non-Archimedean 2-Normed Spaces. Journal of The Chungcheong Mathematical Society, Vol 22, No. 1: 65-71.
Hahng-Yun Chu and Se-Hyun Ku. 2013. A Mazur-Ulam Theorem problem in non-Archimedean n-Normed Spaces. Jounal of Inequalities and Applications, 2013, 34: 1-10.
A.C.M. Rooij. 1978. Non-Archimedean Functional Analysus. New York and Besel, Marcel Dekker Inc.