Semigroups of class Co on l2(Z)


  • Yolanda Santiago Ayala Fac. Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Lima-Perú.



l2(Z) space, Hellinger-Toeplitz theorem, generalized multipli- cation operator, Semigroup of contraction, graph norm


In this work we begin by studying the generalized multiplication operator M on the l2(Z). 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 l2(Z) space with n even and demonstrate that it forms a contraction semigroup of class Co, 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.


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How to Cite

Santiago Ayala, Y. (2023). Semigroups of class Co on l2(Z). Selecciones Matemáticas, 10(02), 273 - 284.

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