Semigrupo de contracción en el espacio l²(Z)

• DOI: 10.22533/at.ed.2792329112

• Palavras-chave: espaço l 2 (Z); teorema de Hellinger-Toeplitz; Semigrupo de contração; existência de solução; norma do gráfico.

• Keywords: Keywords: l 2 (Z) space; Hellinger-Toeplitz theorem; Semigroup of contraction; existence of solution; graph norm

• Abstract:

  In this work we begin by studying the multiplication operator M on the l 2 (Z) space.We prove that this operator is not bounded, is densely defined and symmetric and therefore does not admit a symmetric linear extension to the entire space. We introduce a family of operators on the l 2 (Z) space and demonstrate that it forms a contraction semigroup of class C o ,having -M as its infinitesimal generator. We also prove that if we restrict the domains of that family of operators, they still remain a contraction semigroup. Finally, we give results of existence of solution of the associated abstract Cauchy problem and properties of continuous dependence of the solution in connection to other norms.