Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

BEST APPROXIMATIONS AND ORTHOGONALITIES IN 2κ-INNER PRODUCT SPACES

  • Published : 2006.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, some characterizations of representation for continuous linear functionals on $2{\kappa}$-inner product spaces in terms of best approximations and orthogonalities are given.

Keywords

References

  1. M. Crasmareanu, Projections on complete, finite-dimensional Riemannian man- ifolds, An. Univ. Timisoara, Ser. Mat.-Inform. 33 (1995), 185-194
  2. M. Crasmareanu and S. S. Dragomir, 2k-inner products and 2k-Riemannian Metrics, RGMIA Res. Rep. Coll. 18 (2000)
  3. M. Crasmareanu and S. S. Dragomir, 2k-inner products in real linear spaces, Demonstratio Math. 35 (2002), no. 3, 645-56
  4. S. S. Dragomir, A characterization of elements of best approximation in real normed linear spaces, Studia Univ. Babes-Bolyai Math. 33 (1988), no. 3, 74-80
  5. S. S. Dragomir, Repersentation of continuous linear functionals on complete SQ-inner- product spaces, An. Univ. Timisoara Ser. Stiint. Mat. 30 (1992), 241-250
  6. S. S. Dragomir and I. Muntean, Linear and continuous functional on complete Q-inner product spaces, Babes-Bolyai Univ. Sem. Math. Anal. 7 (1987), 59-68
  7. S. S. Dragomir and N. M. Ionescu, New properties of Q-inner-product spaces, Zb. Rad. (Kragujevac) 14 (1993), 19-24
  8. R. C. James, Orthogonality and linear functionals in normed linear spaces, Trans. Amer. Math. Soc. 61 (1947), 265-292 https://doi.org/10.2307/1990220
  9. S. S. Kim, Y. J. Cho, and S. S. Dragomir, Orthogonalities and decomposition theorems for 2k-normed spaces and applications, preprint
  10. S. S. Kim, Y. J. Cho, and T. D. Narang, Some remarks on orthogonality and best approximation, Demonstratio Math. 30 (1997), no. 2, 293-300
  11. I. Singer, Best Approximation in Normed Linear Spaces by elements of Linear Subspaces, Springer-Verlag, New York, 1970