Conditions ensuring "T..." (Y) <Y

• Autores: Dagmar Medková
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 20, Nº 1, 2005, págs. 43-50
• Idioma: inglés
• Títulos paralelos:
  • Condiciones que aseguran que T-1(Y) < Y
• Enlaces
  • Texto completo  1    2 (pdf) 
• Resumen

  • The following theorem is the main result of the paper: Let X be a complex Banach space and T belong to L(X). Suppose that 0 lies at the unbounded component of the set of those l such that lI - T is a Fredholm operator. Let Y be a dense subspace of the dual space X' and S be a closed operator from Y to X such that T'(Y) is contained in Y and TSy = ST'y for every y belonging to Y. Then for every vector x belonging to X', T'x belongs to Y if and only if x belongs to Y.