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SUMMARY:Pseudospectra and finite sections - A survey on the Banach space c
 ase - Markus Seidel (TU Chemnitz)
DTSTART:20121108T150000Z
DTEND:20121108T160000Z
UID:TALK39633@talks.cam.ac.uk
CONTACT:Dr Hansen
DESCRIPTION:During the last years pseudospectra have become increasingly p
 opular and have lead to interesting results especially for operators on Hi
 lbert spaces. In the more general context of Banach spaces additional diff
 iculties occur\, among them the fact\, which was observed by Shargorodsky\
 , that the robustness of pseudospectra under perturbations can get lost.\n
 In the first part of this talk I want to discuss how the recently introduc
 ed concept of (N\,epsilon)-pseudospectra permits to overcome this drawback
  in a sense and to extend a couple of interesting results beyond the Hilbe
 rt space world.\nIn the second part we pick up the well known observation 
 that passing from an operator A to its finite sections can cause additiona
 l components in the respective pseudospectra. I want to present an algebra
 ic framework which can provide an explanation for this phenomenon for seve
 ral classes of operators.
LOCATION:MR 14\, CMS
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