본문 바로가기
KERD
논문KCI 등재

MAPS PRESERVING GENERALIZED PROJECTION OPERATORS

Hassane Benbouziane|Kaddour Chadli|Mustapha Ech-cherif El Kettani
대한수학회 (The Korean Mathematical Society)|2024.07|대한수학회논문집 (Communications of the KMS)|제39권 제3호|pp. 717-729|DOI 10.4134/CKMS.c230321

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

Hilbert spacegeneralized projectionpreserver
주제분류수학

초록

Let B(H) be the algebra of all bounded linear operators on a Hilbert space H with dim(H) > 2. Let GP(H) be the subset of B(H) of all generalized projection operators. In this paper, we give a complete characterization of surjective maps Φ : B(H) → B(H) satisfying A−λB ∈ GP(H) ⇔ Φ(A) − λΦ(B) ∈ GP(H) for any A,B ∈ B(H) and λ ∈ C.

Abstract

Let B(H) be the algebra of all bounded linear operators on a Hilbert space H with dim(H) > 2. Let GP(H) be the subset of B(H) of all generalized projection operators. In this paper, we give a complete characterization of surjective maps Φ : B(H) → B(H) satisfying A−λB ∈ GP(H) ⇔ Φ(A) − λΦ(B) ∈ GP(H) for any A,B ∈ B(H) and λ ∈ C.

참고문헌 (24)

  1. J. K. Baksalary, "On some linear combinations of hypergeneralized projectors", Linear Algebra Appl, 413(2-3), pp.264~273 (2006)[DOI]
  2. J. Baksalary, "Further properties of generalized and hypergeneralized projectors", Linear Algebra Appl, 389, pp.295~303 (2004)[DOI]
  3. J. K. Baksalary, "Further results on generalized and hypergeneralized projectors", Linear Algebra Appl, 429(5-6), pp.1038~1050 (2008)[DOI]
  4. J. K. Baksalary, "An alternative characterization of generalized projectors", Linear Algebra Appl, 388, pp.61~65 (2004)[DOI]
  5. M. Breˇsar, "Linear preservers on B(X), Linear operators", pp.49~58 (1994), Polish Acad. Sci. Inst. Math
  6. A. Chahbi, "On linear maps that preserve the generalized projection in separable hilbert space", Math-Recherche & Applications, 15, pp.44~49 (2016)
  7. G. Dolinar, "Maps on B(H)preserving idempotents", Linear Multilinear Algebra, 52(5), pp.335~347 (2004)[DOI]
  8. M. P. Drazin, "Natural structures on semigroups with involution", Bull. Amer. Math. Soc, 84(1), pp.139~141 (1978)[DOI]
  9. H. -K. Du, "The spectral characterization of generalized projections", Linear Algebra Appl, 400, pp.313~318 (2005)[DOI]
  10. F. G. Frobenius, "Uber die Darstellung der endlichen Gruppen durch lineare Substitutionen" (1897)
  11. J. Groß, "Remarks on the sharp partial order and the ordering of squares of matrices", Linear Algebra Appl, 417(1), pp.87~93 (2006)[DOI]
  12. J. Groß, "Generalized and hypergeneralized projectors", Linear Algebra Appl, 264, pp.463~474 (1997)[DOI]
  13. S. Kabbaj, "Linear maps preserving the generalized projection", Thai J. Math, 13(2), pp.381~389 (2015)
  14. L. Lebtahi, "A note on k-generalized projections", Linear Algebra Appl, 420(2-3), pp.572~575 (2007)[DOI]
  15. X. M. Li, "Maps on B(H)preserving projections", Adv. Math. (China), 43(3), pp.425~428 (2014)
  16. J. Mashreghi, "Invariant Subspaces of the Shift Operator", Contemporary Mathematics, 638 (2015), Amer. Math. Soc[DOI]
  17. L. Moln´ar, "Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces" (2007), Springer
  18. A. N. Motlagh, "Linear maps on B(H)preserving some operator properties", Proyecciones, 40(6), pp.1357~1365 (2021)
  19. G. J. Murphy, "C∗-Algebras and Operator Theory" (1990), Academic Press, Inc
  20. C. Pearcy, "Sums of small numbers of idempotents", Michigan Math. J, 14, pp.453~465 (1967)
  21. S. Radosavljevi´c, "On pairs of generalized and hypergeneralized projections in a Hilbert space", Funct. Anal. Approx. Comput, 5(2), pp.67~75 (2013)
  22. G. W. Stewart, "A note on generalized and hypergeneralized projectors", Linear Algebra Appl, 412(2-3), pp.408~411 (2006)[DOI]
  23. U. Uhlhorn, "Representation of symmetry transformations in quantum mechanics", Arkiv Fysik, 23, pp.307~340 (1963)
  24. L. Yang, "Maps on B(H)preserving involution", Linear Algebra Appl, 431(5-7), pp.666~672 (2009)[DOI]

관련 논문AI추천

Maps preserving $m$- isometries on Hilbert spaceAlireza Majidi강원경기수학회 · 한국수학논문집2019 · 제27권 제3호LINEAR MAPS PRESERVING IDEMPOTENT OPERATORSAli Taghavi, Roja Hosseinzadeh대한수학회 · 대한수학회보2010 · 제47권 제4호Linear maps preserving AN-operatorsHiroyuki Osaka, Ramesh Golla대한수학회 · 대한수학회보2020 · 제57권 제4호MAPS PRESERVING SOME MULTIPLICATIVE STRUCTURES ON STANDARD JORDAN OPERATOR ALGEBRASShirin Hejazian, Somaye Ghorbanipour대한수학회 · 대한수학회지2017 · 제54권 제2호MAPS PRESERVING η-PRODUCT A*B + ηBA* ON C*-ALGEBRASAli Taghavi, Haji Mohammad Nazari, Hamid Rohi, Vahid Darvish대한수학회 · 대한수학회지2017 · 제54권 제3호Jordan Product and ∂-Spectrum PreserversEl Houcine El Bouchibti, Youssef Chakir경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2025 · 제65권 제2호

이 간행물의 다른 논문 (17건)

The Chow ring of a sequence of point blow-upsDaniel Camazon Portelapp. 563-574(m, n)-CLOSED δ-PRIMARY IDEALS IN AMALGAMATIONMohammad Hamoda, Mohammed Issoualpp. 575-583ON η−GENERALIZED DERIVATIONS IN RINGS WITH JORDAN INVOLUTIONPhool Miyanpp. 585-593On differential identities involving partitioning ideals of semiringsMuhammad Aslam, Ghulam Farid, Tariq Mahmood, Liaqat Alipp. 595-609On nonnil-$m$-formally Noetherian ringsAbdelamir Dabbabi, Ahmed Maatallahpp. 611-622
원문 보기