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The Some Ultranorm Spaces and Isomorphicity

Year 2020, Volume: 7 Issue: 1, 265 - 272, 28.06.2020
https://doi.org/10.35193/bseufbd.670679

Abstract

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.

References

  • [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.

Bazı Ultranormlu Uzaylar ve İzomorfikliği

Year 2020, Volume: 7 Issue: 1, 265 - 272, 28.06.2020
https://doi.org/10.35193/bseufbd.670679

Abstract

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.

References

  • [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.
There are 13 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

İbrahim Şanlıbaba 0000-0001-8801-464X

Publication Date June 28, 2020
Submission Date March 4, 2020
Acceptance Date June 1, 2020
Published in Issue Year 2020 Volume: 7 Issue: 1

Cite

APA Şanlıbaba, İ. (2020). Bazı Ultranormlu Uzaylar ve İzomorfikliği. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, 7(1), 265-272. https://doi.org/10.35193/bseufbd.670679