SavedAdd your journal

Journals / European Journal of Pure and Applied Mathematics (elektronik) / 2010 / Cilt: 3 - Sayı: 4

Fredholmness of combinations of two idempotents

Tao XIE
Kezheng ZUO
Pages
678–685
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

If P and Q are two idempotents on a Hilbert space, in this paper, we prove that Fredholmness of aP + bQ − cPQ is independent of the choice of a, b, c with ab $neq$ 0. 2000 Mathematics Subject Classifications: 15A03, 15A24

📌 3 Key Takeaways

🎯
Objective & Hypothesis:If P and Q are two idempotents on a Hilbert space, in this paper, we prove that Fredholmness of aP + bQ − cPQ is independent of the choice of a, b, c with ab $neq$ 0. 2000 Mathematics Subject Classifications: 15A03, 15A24
📊
Key Findings & Data:If P and Q are two idempotents on a Hilbert space, in this paper, we prove that Fredholmness of aP + bQ − cPQ is independent of the choice of a, b, c with ab $neq$ 0. 2000 Mathematics Subject Classifications: 15A03, 15A24
💡
Conclusion & Impact:If P and Q are two idempotents on a Hilbert space, in this paper, we prove that Fredholmness of aP + bQ − cPQ is independent of the choice of a, b, c with ab $neq$ 0. 2000 Mathematics Subject Classifications: 15A03, 15A24
🔬Design:Research Article
📍Scope:2000 Verileri
⚙️Variables:Domain Parameters

Abstract

If P and Q are two idempotents on a Hilbert space, in this paper, we prove that Fredholmness of aP + bQ − cPQ is independent of the choice of a, b, c with ab $neq$ 0. 2000 Mathematics Subject Classifications: 15A03, 15A24

🔖

Cite This Article

XIE, T., ZUO, K. (2022). Fredholmness of combinations of two idempotents. European Journal of Pure and Applied Mathematics (elektronik), Cilt: 3 - Sayı: 4, 678–685. https://ajindex.com/articles/511328

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (19)

  1. J.K. Baksalary and O.M. Baksalary. Nonsingularity of linear combinations of idempotent matrices. Linear Algebra and its Applications, 388: 25-29, 2004
  2. J.K. Baksalary and O.M. Baksalary. Idempotency of linear combinations of three idempotent matrices, two of which are disjoint. Linear Algebra and its Applications 388: 67-78, 2004
  3. J.B. Conway. A Course in Functional Analysis, 2nd ed., Springer, New York, 1990
  4. H. Du, X. Yao and C. Deng. Invertibility of linear combinations of two idempotents. Proceedings of American Mathematical Society, 134: 1451-1457, 2006
  5. P.A. Fillmore. On sums of projections. Journal of Functional Analysis, 4: 146-152, 1969
  6. J. Gro and G. Trenkler. Nonsingularity of the difference of two oblique projectors. SIAM J. Matrix Anal. Appl., 21: 390-395, 1999
  7. H.L. Gau and P.Y. Wu. Fredholmness of linear combinations of two idempotents. Integral Equations and Opertor Theory, 59: 579-583, 2007
  8. H.L. Gau, C.J. Wang and N.C. Wong. Invertibility and Fredholmness of linear combinations of quadratic, k-potent and nilpotent operators. Operators and Matrices, 2: 193-199, 2008
  9. R. Harte, Invertibility and Singularity for Bounded Linear Operators, Marcel Dekker, New York and Basel, 1988
  10. J.J. Koliha and V. Rakocevic. Invertibility of the sum of idempotents. Linear and Multilinear Algebra, 50: 285-292, 2002
  11. J.J. Koliha and V. Rakocevic. Invertibility of the difference of idempotents. Linear and Multilinear Algebra, 51: 97-110, 2003
  12. J.J. Koliha and V. Rakocevic. I.Straˇskraba. The difference and sum of projectors. Linear Algebra Appl., 388: 279-288, 2004
  13. J.J. Koliha and V. Rakocevic. Fredholm properties of the difference of orthogonal projections in a Hilbert space. Integr. Equ. Oper. Theory, 52: 125-134, 2005
  14. J.J. Koliha and V. Rakocevic. The nullity and rank of linear combinations of idempotent matrices. Linear Algebra Appl., 418: 11-14, 2006
  15. J.J. Koliha and V. Rakocevics. Stability theorems for linear combinations of idempotents. Integr. Equ. Oper. Theory, 58: 597-601, 2007
  16. C. Pearcy and D. Topping. Sums of small numbers of idempotents. Michigan Journal of Mathematics, 14(4): 453-465, 1967
  17. V. Rabanovic. Every matrix is a linear combination of three idempotents. Linear Algebra and its Applications, 390: 137-143, 2004
  18. P.Y. Wu. Sums of idempotent matrices. Linear Algebra and its Applications, 142: 43-54, 1990
  19. P.Y. Wu. Additive combinations of special operation