Automatic continuity for linear surjective mappings decreasing the local spectral radius at some fixed vector

作者：Costara Constantin^*

来源：Archiv der Mathematik, 2010, 95(6): 567-573.

DOI：10.1007/s00013-010-0191-4

• Automatic continuity
• Local spectrum
• Local spectral radius

Let X be a complex Banach space and denote by L(X) the space of bounded linear operators on X. Let e be a nonzero element of X. We prove that if phi is a linear and surjective mapping from L(X) into itself which decreases into itself which decreases the local spectral radius at e, then phi is automatically continuous.

• 出版日期2010-12