Mediterranean Journal of Mathematics

, Volume 13, Issue 4, pp 2039–2059 | Cite as

Left- and Right-Atkinson Linear Relation Matrices

  • Teresa Álvarez
  • Yosra Chamkha
  • Maher Mnif


Let X and Y be Banach spaces. When A and B are linear relations in X and Y, respectively, we denote by M C the linear relation in X × Y of the form \( M_c = \Big(\begin{array}{ll} A & C \\ 0 & B \end{array}\Big)\), where 0 is the zero operator from X to Y and C is a bounded operator from Y to X. The goal of this paper is to present some necessary and sufficient conditions on A and B such that there exists a bounded operator C from Y to X for which M C is a Browder linear relation in X × Y.


Left-Atkinson relation right-Atkinson relation upper triangular linear relation matrix 

Mathematics Subject Classification

47A06 47A53 47A55 


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© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OviedoOviedoSpain
  2. 2.Département de Mathématiques, Faculté des Sciences de SfaxUniversité de SfaxSfaxTunisie

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