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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 683021, 14 pages
http://dx.doi.org/10.1155/2012/683021
Research Article

The Maximal Subspace for Generation of -Regularized Families

1Facultad de Ciencias Básicas, Universidad Tecnológica de Bolívar, Cartagena, Colombia
2Departamento de Matemática y Ciencia de la Computación, Facultad de Ciencia, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile

Received 25 May 2012; Revised 7 September 2012; Accepted 12 September 2012

Academic Editor: Patricia J. Y. Wong

Copyright © 2012 Edgardo Alvarez-Pardo and Carlos Lizama. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be a linear operator in a Banach space . We define a subspace of and a norm such that the part of in such subspace generates an (, )-regularized resolvent family. This space is maximal-unique in a suitable sense and nontrivial, under certain conditions on the kernels and .