ELA, Volume 16, pp. 216-231, August 2007, abstract.

Spectrum of Infinite Block Matrices and pi-Triangular Operators

M. I. Gil'

The paper deals with infinite block matrices having compact off 
diagonal parts. Bounds for the spectrum are established and 
estimates for the norm of the resolvent are proposed. Applications 
to matrix integral operators are also discussed. The main tool is 
the pi-triangular operators defined in the paper.