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Articles

On the invertibility and range closedness of the linear combinations of a pair of projections

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Pages 613-622 | Received 01 Mar 2016, Accepted 02 Jun 2016, Published online: 26 Jun 2016

References

  • Conway J. A course in functional analysis. New York (NY): Springer-Verlag; 1990.
  • Baksalary OM, Trenkler G. Revisitation of the product of two orthogonal projectors. Linear Algebra Appl. 2009;430:2813–2833.
  • Böttcher A, Spitkovsky I. A gentle guide to the basics of two projections theory. Linear Algebra Appl. 2010;432:1412–1459.
  • Buckholtz D. Hilbert space idempotents and involutions. Proc. Am. Math. Soc. 2000;128:1415–1418.
  • Deng C, Cvetković-Ilić DS, Wei YM. On invertibility of combinations of k-potent operators. Linear Algebra Appl. 2012;437:376–387.
  • Deng C. On the invertibility of Hilbert space idempotents. Acta Math. Sci. 2014;34B:523–536.
  • Deng C. Invertibility and stability of linear combinations of m-potent operators. Linear Multilinear Algebra. 2014;62:1365–1376.
  • Douglas RG. On majorization, factorization, and range inclusion of operators on Hilbert spaces. Proc. Am. Math. Soc. 1966;17:413–416.
  • Khadivi M. Range inclusion and operator equations. J. Math. Anal. Appl. 1996;197:630–633.
  • Fillmore PA, Williams IP. On operator ranges. Adv. Math. 1971;7:254–281.
  • Du H, Deng C. A new characterization of gaps between two subspaces. Proc. Am. Math. Soc. 2005;133:3065–3070.
  • Halmos P. Two subspaces. Trans. Am. Math. Soc. 1969;144:381–389.
  • Buckholtz D. Inverting the difference of Hilbert space projections. Am. Math. Mon. 1997;104:60–61.
  • Koliha JJ, Rakočević V. Invertibility of the difference of idempotents. Linear Multilinear Algebra. 2003;51:97–110.
  • Liu XJ, Wu LL, Yu YM. The group inverse of the combinations of two idempotent matrices. Linear Multilinear Algebra. 2011;59:101–115.
  • Tian Y. A disjoint idempotent decomposition for linear combinations produced from two commutative tripotent matrices and its applications. Linear Multilinear Algebra. 2011;59:1237–1246.

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