Spectral continuity

The map which takes a bounded operator to its spectrum, is upper semicontinuous, but its continuity points form a proper dense. Two problems thus arise:

  • at which points of B(H) is F in fact continuous
  • what continuity-type properties hold.

Requirements: Functional analysis, subharmonic functions and possibly several complex variables. References: [1] B. Aupetit, A primer on spectral theory, Springer-Verlag, New York, 1991. [2] J.B. Conway & B.B. Morrel, Operators that are points of spectral continuity, Integral Equations and Operator Theory 2 (1979), 174-198.