Maps preserving Fredholm or semi-Fredholm elements relative to some ideal

• Mohadeseh Rostamani ^[1] ; Shirin Hejazian ^[1]
  1. [1] Ferdowsi University of Mashhad

     Ferdowsi University of Mashhad

     Irán

     
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 17, Nº. 1, 2015, págs. 29-40
• Idioma: inglés
• DOI: 10.4067/S0719-06462015000100003
• Enlaces
  • Texto completo
• Resumen
  • español

    Consideramos el álgebra de Calkin C R(A) y la teoría de Fredholm en un álgebra de Banach A relativa a algún ideal fijo F de A. Nuestra meta es estudiar aplicaciones lineales entre álgebras de Banach unitales A y B las cuales son sobrejectivas salvo los elementos no esenciales relativos a F y preservan los elementos de Fredholm o semi-Fredholm en ambas direcciones o equivalentemente conjuntos espectrales esenciales relativos diferentes tales como el espectro esencial izquierdo o derecho, la frontera del espectro esencial o el espectro esencial completo. Caracterizamos dichas aplicaciones cuando uno de los C R(A) o C R(B) es conmutativo e investigamos problemas similares cuando A se asume que es una C*-álgebra unital de rango real cero y B es una álgebra de Banach cualquiera.

  • English

    We consider the Calkin algebra C R(A) and the Fredholm theory in a Banach algebra A, relative to some fixed ideal F of A. Our aim is to study linear maps between unital Banach algebras A and B which are surjective up to the inessential elements relative to F, and preserve Fredholm or semi-Fredholm elements in both directions or equivalently different relatively essential spectral sets such as essential spectrum, left or right essential spectrum, the boundary of essential spectrum or the full essential spectrum. We characterize such mappings when one of C R(A) or C R(B) is commutative and also investigate similar problems when A is assumed to be a unital C*-algebra of real rank zero and B is an arbitrary Banach algebra.

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