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The Orthogonal Projection and the Riesz Representation Theorem Cover

The Orthogonal Projection and the Riesz Representation Theorem

Formalized Mathematics
Volume 23 (2015): Issue 3 (September 2015)
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Open Access
|Sep 2015
References

References

  1. [1] Grzegorz Bancerek. The fundamental properties of natural numbers., 1(1):41-46, 1990.
    Search in Google Scholar
  2. [2] Grzegorz Bancerek. The ordinal numbers., 1(1):91-96, 1990.
    Search in Google Scholar
  3. [3] Haim Brezis. Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer, 2011.
    Open DOISearch in Google Scholar
  4. [4] Czesław Bylinski. The complex numbers., 1(3):507-513, 1990.
    Search in Google Scholar
  5. [5] Czesław Bylinski. Functions and their basic properties., 1(1): 55-65, 1990.
    Search in Google Scholar
  6. [6] Czesław Bylinski. Functions from a set to a set., 1(1):153-164, 1990.
    Search in Google Scholar
  7. [7] Czesław Bylinski. Partial functions., 1(2):357-367, 1990.
    Search in Google Scholar
  8. [8] Czesław Bylinski. Some basic properties of sets., 1(1):47-53, 1990.
    Search in Google Scholar
  9. [9] Peter D. Dax. Functional Analysis. Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts. Wiley Interscience, 2002.
    Search in Google Scholar
  10. [10] Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Subspaces and cosets of subspace of real unitary space., 11(1):1-7, 2003.
    Search in Google Scholar
  11. [11] Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Topology of real unitary space., 11(1):33-38, 2003.
    Search in Google Scholar
  12. [12] Noboru Endou, Yasumasa Suzuki, and Yasunari Shidama. Real linear space of real sequences., 11(3):249-253, 2003.
    Search in Google Scholar
  13. [13] Jarosław Kotowicz. Convergent sequences and the limit of sequences., 1(2):273-275, 1990.
    Search in Google Scholar
  14. [14] Jarosław Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers., 1(3):477-481, 1990.
    Search in Google Scholar
  15. [15] Keiko Narita, Noboru Endou, and Yasunari Shidama. Dual spaces and Hahn-Banach theorem., 22(1):69-77, 2014. doi:10.2478/forma-2014-0007.
    Open DOISearch in Google Scholar
  16. [16] Adam Naumowicz. Conjugate sequences, bounded complex sequences and convergent complex sequences., 6(2):265-268, 1997.
    Search in Google Scholar
  17. [17] Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces., 12(3):269-275, 2004.
    Search in Google Scholar
  18. [18] Bogdan Nowak and Andrzej Trybulec. Hahn-Banach theorem., 4(1):29-34, 1993.
    Search in Google Scholar
  19. [19] Jan Popiołek. Some properties of functions modul and signum., 1(2):263-264, 1990.
    Search in Google Scholar
  20. [20] Jan Popiołek. Introduction to Banach and Hilbert spaces - part I., 2(4):511-516, 1991.
    Search in Google Scholar
  21. [21] Jan Popiołek. Introduction to Banach and Hilbert spaces - part II., 2(4):517-521, 1991.
    Search in Google Scholar
  22. [22] Jan Popiołek. Introduction to Banach and Hilbert spaces - part III., 2(4):523-526, 1991.
    Search in Google Scholar
  23. [23] Jan Popiołek. Real normed space., 2(1):111-115, 1991.
    Search in Google Scholar
  24. [24] Walter Rudin. Functional Analysis. New York, McGraw-Hill, 2nd edition, 1991.
    Search in Google Scholar
  25. [25] Yasunari Shidama. Banach space of bounded linear operators., 12(1):39-48, 2004.
    Search in Google Scholar
  26. [26] Yasumasa Suzuki, Noboru Endou, and Yasunari Shidama. Banach space of absolute summable real sequences., 11(4):377-380, 2003.
    Search in Google Scholar
  27. [27] Andrzej Trybulec. Binary operations applied to functions., 1 (2):329-334, 1990.
    Search in Google Scholar
  28. [28] Andrzej Trybulec. On the sets inhabited by numbers., 11(4): 341-347, 2003.
    Search in Google Scholar
  29. [29] Andrzej Trybulec and Czesław Bylinski. Some properties of real numbers., 1(3):445-449, 1990.
    Search in Google Scholar
  30. [30] Wojciech A. Trybulec. Subspaces and cosets of subspaces in real linear space., 1(2):297-301, 1990.
    Search in Google Scholar
  31. [31] Wojciech A. Trybulec. Vectors in real linear space., 1(2):291-296, 1990.
    Search in Google Scholar
  32. [32] Zinaida Trybulec. Properties of subsets., 1(1):67-71, 1990.
    Search in Google Scholar
  33. [33] Edmund Woronowicz. Relations and their basic properties., 1 (1):73-83, 1990.
    Search in Google Scholar
  34. [34] Edmund Woronowicz. Relations defined on sets., 1(1):181-186, 1990.
    Search in Google Scholar
  35. [35] Hiroshi Yamazaki, Yasumasa Suzuki, Takao Inou´e, and Yasunari Shidama. On some properties of real Hilbert space. Part I., 11(3):225-229, 2003.
    Search in Google Scholar
  36. [36] Kosaku Yoshida. Functional Analysis. Springer, 1980.
    Search in Google Scholar
DOI: https://doi.org/10.1515/forma-2015-0020 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
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Language: English
Page range: 243 - 252
Submitted on: Jul 1, 2015
Published on: Sep 30, 2015
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Keywords:
normed linear spaces,
Banach spaces,
duality,
orthogonal projection,
Riesz representation
MSC:
46E20,
46C15,
03B35
MML:
DUALSP04
Related subjects:
Computer sciences,
Artificial intelligence,
Computer sciences, other,
Mathematics,
Logic and set theory,
General mathematics

© 2015 Keiko Narita, Noboru Endou, Yasunari Shidama, published by University of Białystok
This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.

Volume 23 (2015): Issue 3 (September 2015)
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