Surjective maps preserving the reduced minimum modulus of products

• Autores: Sepide Hajighasemi, Shirin Hejazian
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 25, Nº. 1, 2023, págs. 139-150
• Idioma: inglés
• DOI: 10.56754/0719-0646.2501.139
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen Suponga que 𝔅(H) es el álgebra de Banach de todos los operadores lineales acotados en un espacio de Hilbert H con dim(H) ≥ 3. Denote por γ(.) el módulo mínimo reducido de un operador. Caracterizamos las aplicaciones sobreyectivas φ en 𝔅(H) que satisfacen γ(φ(T )φ(S)) = γ(T S) (T, S ∈ 𝔅 (H)). También entregamos la forma general de las aplicaciones sobreyectivas en 𝔅(H) que preservan el módulo mínimo reducido de productos triples de Jordan de operadores. 2020 AMS Mathematics Subject Classification: 47A10, 47A13, 47A25, 47B02, 47B49.

  • English

    Suppose ?(H) is the Banach algebra of all bounded linear operators on a Hilbert space H with dim(H) ≥ 3. Let γ(.) denote the reduced minimum modulus of an operator. We charaterize surjective maps φ on ? (H) satisfying γ(φ(T )φ(S)) = γ(T S) (T, S ∈ ? (H)).

    Also, we give the general form of surjective maps on ?(H) preserving the reduced minimum modulus of Jordan triple products of operators.

• Referencias bibliográficas
  • Apostol, C.. (1985). The reduced minimum modulus. Michigan Math. J.. 32. 279
  • Bourhim, A.. (2012). Additive maps preserving the reduced minimum modulus of Banach space operators. J. Operator Theory. 279
  • Bourhim, A.,Burgos, M.,Shulman, V. S.. (2010). Linear maps preserving the minimum and reduced minimum moduli. J. Funct. Anal.. 258. 50-66
  • Brešar, M.,Šemrl, P.. (2020). Linear and multilinear algebra and function spaces. American Mathematical Society. Providence, RI.
  • Costara, C.. (2016). On nonlinear maps preserving the reduced minimum modulus on differences of matrices. Linear Algebra Appl.. 507. 288
  • Cui, J.,Hou, J.. (2008). Maps leaving functional values of operator products invariant. Linear Algebra Appl.. 428. 1649
  • Dobovišek, M.,Kuzma, B.,Lešnjak, G.,Li, C. K.,Petek, T.. (2007). Mappings that preserve pairs of operators with zero triple Jordan product....
  • Harte, R.,Mbekhta, M.. (1993). Generalized inverses in C∗-algebras II. Studia Mathematica. 106. 129
  • Mashreghi, J.,Stepanyan, A.. (2016). Nonlinear maps preserving the reduced minimum modulus of operators. Linear Algebra Appl.. 493. 426
  • Mbekhta, M.. (2007). Linear maps preserving the generalized spectrum. Extracta Math.. 22. 45-54
  • Molnár, L.. (2007). Selected preserver problems on algebraic structures of linear operators and on function spaces. Springer-Verlag. Berlin....
  • Müller, V.. (2007). Spectral theory of linear operators and spectral systems in Banach algebras, Operator Theory. Birkhäuser Verlag. Basel.
  • Skhiri, H.. (2008). Reduced minimum modulus preserving in Banach space. Integral Equations Operator Theory. 62. 137