The Some Ultranorm Spaces and Isomorphicity

Yıl 2020, Cilt: 7 Sayı: 1, 265 - 272, 28.06.2020

İbrahim Şanlıbaba

https://doi.org/10.35193/bseufbd.670679

Öz

In this study metric spaces, ultrametric spaces, normed spaces and ultranormed spaces are introduced and their relations between each other and examples are shown. Isometry and ultra isometry are defined in ultranormed spaces. Then some example of ultra-normed spaces are given and it is shown to be ultra Banach space and is isomorphic.

Anahtar Kelimeler

Ultrametric, Ultranorm, Krull Sharpening, Ultra Isometry, Ultra Banach Spaces

Bazı Ultranormlu Uzaylar ve İzomorfikliği

Öz

Bu çalışmada metrik uzaylar, ultrametrik uzayları, normlu uzaylar ve ultranormlu uzaylar tanıtılıp aralarındaki ilişkiler ve örnekleri gösterildi. Ultranormlu uzaylarda izometri ve ultra izometri tanımları yapıldı. Sonra bazı ultranormlu uzaylara örnekler verilip ultra Banach uzay olduğu ve izomorfik olduğu gösterildi.

Anahtar Kelimeler

Ultrametrik, Ultranorm, Krull Sharpening, Ultra izometri, Ultra Banach Spaces

Kaynakça

• [1] Diagana, T. (2006). An Introduction to Classical and p-ADIC Theory of Linear Operators and Applications, by Nova Science Publishers Inc, ISBN 1-59454-424-7, New York.
• [2] Krull, W. (1998). Ultrametric Triangle Inequality. Planet Math, Göttingen 1959.Li, G., Hart, A. ve Gregory, J., Flocculation and sedimentation, 295, Technomics Press. Lancaster PA.
• [3] Ludkovsky. S., and Diarra, B. (2002). Spectral Integration and Spectral Theory for Non-Arcimedean Banach Spaces IJMMS 31,7, 421-442.
• [4] Şanlıbaba, I. (2014). Ultrametric Banach space isomorphic to new spaces, Master’s thesis. Nevşehir Hacı Bektaş Veli University, Nevşehir.
• [5] Bayraktar, M. (2006). Fonsiyonel Analiz. Gazi Kitabevi. Ankara.
• [6] Nesin, A. (2012). Analiz IV. Nesin Matematik Köyü, İstanbul.
• [7] Gajic, L. (2001). On Ultrametric Space, Novi Sad J. Match. 31, 2, 69-71.
• [8] Diagana, T. (2006). c_0-Semigroups of Linear Operators on some Ultrametrıc Banach Space. IJMMS, DOI10. 1155/2006/52398.
• [9] Diagana, T. (2007). Non-Arcimedean Linear Operators and Applications, by Nova Science Publishers Inc. ISBN 1-60021-405-3, New York.
• [10] Diarra B. (1998). An Operatör on Ultrametric Hilbert Spaces. Journal of Analysis 6, 55-74.
• [11] Kaplansky, I. (1972). Set Theory and Metric Spaces. AMS Chelsea Publishing, ISBN 0-8218-2694-8.
• [12] Perez-Garcia, C., Schikhof, W. H. (2010). Locally Convex Spaces over Non-Archimedean Valued Fields. Cambridge University Press, 978-0-521-19243-9.
• [13] Havinga, M. (2011). Ultrametric Matrices, Korteweg-de Vries Institute for Mathematics Faculty of Science. 5-14, 13.