Annals of Functional Analysis

Cone nonnegativity of Moore–Penrose inverses of unbounded Gram operators

T. Kurmayya and G. Ramesh

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In this article, necessary and sufficient conditions for the cone nonnegativity of Moore–Penrose inverses of unbounded Gram operators are derived. These conditions include statements on acuteness of certain closed convex cones in infinite-dimensional real Hilbert spaces.

Article information

Ann. Funct. Anal., Volume 7, Number 2 (2016), 338-347.

Received: 21 September 2015
Accepted: 4 October 2015
First available in Project Euclid: 8 April 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 15A09: Matrix inversion, generalized inverses
Secondary: 47H05: Monotone operators and generalizations 15B48: Positive matrices and their generalizations; cones of matrices

Moore–Penrose inverse unbounded Gram operator cone acute cone


Kurmayya, T.; Ramesh, G. Cone nonnegativity of Moore–Penrose inverses of unbounded Gram operators. Ann. Funct. Anal. 7 (2016), no. 2, 338--347. doi:10.1215/20088752-3544417.

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  • [1] A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, 2nd ed., CMS Books Math./Ouvrages Math. SMC 15, Springer, New York, 2003.
  • [2] A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Classics Appl. Math. 9, SIAM, Philadelphia, 1994.
  • [3] A. Cegielski, Obtuse cones and Gram matrices with non-negative inverse, Linear Algebra Appl. 335 (2001), nos. 1–3, 167–181.
  • [4] L. Collatz, Functional Analysis and Numerical Mathematics, Academic, New York, 1966.
  • [5] S. Goldberg, Unbounded Linear Operators: Theory and Applications, McGraw-Hill, New York, 1966.
  • [6] C. W. Groetsch, Stable Approximate Evaluation of Unbounded Operators, Lecture Notes in Math. 1894, Springer, Berlin, 2007.
  • [7] W. J. Kammerer and R. J. Plemmons, Direct iterative methods for least-squares solutions to singular operator equations, J. Math. Anal. Appl. 49 (1975), no. 2, 512–526.
  • [8] S. H. Kulkarni and G. Ramesh, Projection methods for computing Moore–Penrose inverses of unbounded operators, Indian J. Pure Appl. Math. 41 (2010), no. 5, 647–662.
  • [9] S. H. Kulkarni and G. Ramesh, Perturbation of closed range operators and Moore–Penrose inverses, preprint, arXiv:1510.01534v2 [math.FA].
  • [10] T. Kurmayya and K. C. Sivakumar, Nonnegative Moore–Penrose inverses of Gram operators, Linear Algebra Appl. 422 (2007), no. 2–3, 471–476.
  • [11] J.-P. Labrousse, Inverses généralisés d’opérateurs non bornés, Proc. Amer. Math. Soc. 115 (1992), no. 1, 125–129.
  • [12] O. L. Mangasarian, Characterizations of real matrices of monotone kind, SIAM Rev. 10 (1968), no. 4, 439–441.
  • [13] W. Rudin, Functional Analysis, 2nd ed., Internat. Ser. Pure Appl. Math., McGraw-Hill, New York, 1991.
  • [14] K. C. Sivakumar, Range and group monotonicity of operators, Indian J. Pure Appl. Math. 32 (2001), no. 1, 85–89.