Bull. Austral. Math. Soc. 72(3) pp.337--347, 2005.

Bounds for the distance to finite-dimensional subspaces

S.S. Dragomir

Received: 17th January, 2005



We establish upper bounds for the distance to finite-dimensional subspaces in inner product spaces and improve some generalisations of Bessel's inequality obtained by Boas, Bellman and Bombieri. Refinements of the Hadamard inequality for Gram determinants are also given.

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(Metadata: XML, RSS, BibTeX) MathSciNet: MR2199636 Z'blatt-MATH: 1104.46011


  1. R. Bellman;
    Almost orthogonal series,
    Bull. Amer. Math. Soc. 50 (1944), pp. 517--519. MR10639
  2. R.P. Boas;
    A general moment problem,
    Amer. J. Math. 63 (1941), pp. 361--370. MR3848
  3. E. Bombieri;
    A note on the large sieve,
    Acta Arith. 18 (1971), pp. 401--404. MR286773
  4. F. Deutsch;
    Best Approximation in inner product spaces,
    CMS Books in Mathematics (Springer-Verlag, New York, Berlin, Heidelberg, 2001). MR1823556
  5. S.S. Dragomir;
    A counterpart of Bessel's inequality in inner product spaces and some Grüss type related results,
    RGMIA Res. Rep. Coll. 6 (2003).
    Supplement, Article 10. [Online: http://rgmia.vu.edu.au/v6(E).html]
  6. S.S. Dragomir;
    Some Bombieri type inequalities in inner product spaces,
    J. Indones. Math. Soc. 10 (2004), pp. 91--97. MR2097092
  7. S.S. Dragomir;
    On the Boas--Bellman inequality in inner product spaces,
    Bull. Austral. Math. Soc. 69 (2004), pp. 217--225. MR2051357
  8. S.S. Dragomir;
    Advances in inequalities of the Schwarz, Grüss and Bessel type in inner product spaces,
    RGMIA Monographs (2004).
    [Online: http://rgmia.vu.edu.au/monographs/advances.htm]
  9. D.S. Mitrinović, J.E. Pečarić and A.M. Fink;
    Classical and new inequalities in analysis (Kluwer Academic, Dordrecht, 1993). MR1220224

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