The spectral and Fredholm theory of extensions of bounded linear operators

Bruce A. Barnes
1989 Proceedings of the American Mathematical Society  
Assume T is a bounded linear operator on some Banach space Y, and that T has a bounded extension T on another space. In general almost nothing can be said concerning the relationship between the spectral and Fredholm properties of T and T . However, assuming the special condition that the range of T lies in K , it is shown that these properties are essentially the same for T and T .
doi:10.1090/s0002-9939-1989-0955454-4 fatcat:4tkxzue74rf5jatyy4ky3b3rcy