Some fixed points preserver

Subject Areas : Statistics

A. Taghavi ¹ (Department of Mathematical Sciences, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran)
R. Hosseinzadeh ² (Department of Mathematical Sciences, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran Corresponding author)

Received: 2015-09-18 Accepted : 2016-12-18 Published : 2016-02-01

Keywords: مسایل نگهدارنده, جبر عملگرها, نقطه ثابت,

Abstract :

Let B(X) and M (F) n be the algebra of all bounded linear operators on a complex Banachspace X with dimX 3 and the algebra of all n n matrices over a field F with char F  2 ,respectively. Also let F(A) be the space of all fixed points of an operator AB(X) . In thispaper, we characterize the forms of linear maps  :B(X)B(X) which satisfyF(A) = 0F( (A)) = 0 and linear maps :M (F) M (F) n n   which preserve the fixedpoints of matrices

References:

[1] G. Dolinar, S. Du, J. Hou, P. Legiša, General preservers of invariant subspace lattices, Linear Algebra Appl. 429 (2008) 100-109.

[2] A.A. Jafarian, A.R. Sourour, Linear maps that preserve the commutant, double commutant or the lattice of invariant subspaces, Linear Multilinear Algebra 38 (1994) 117–129.

[3] P. Šemrl, Applying projective geometry to transformations on rankone idempotents, Functional Analysis 210 (2004) 248-257.

[4] P. Šemrl, Two characterization of automorphisms on B(X ) , Studia Mathematica 105 (2) (1993) 143-148.

[5] A. Taghavi, R. Hosseinzadeh, Maps preserving the dimension of fixed points of products of operators, Linear Multilinear Algebra 62 (2013) 1285-1292.

[6] A. Taghavi, R. Hosseinzadeh and Hamid Rohi Maps preserving the fixed points of sum of operators, Operators and Matrices 9 (2015) 563-569.

[7] D.Wang, X. Li, H. Ge Idempotent elements determined matrix algebras, Linear Algebra Appl. 435 (2011) 2889- 2895.