Traces and symmetric linear forms

摘要

The famous Calkin theorem says that there is a one- to- one correspondence between all ideals of operators on the separable infinitedimensional Hilbert space and all symmetric ideals ( invariant under permutations) of bounded scalar sequences: A( H). a( N). Being unaware of my method from 1987/ 90 and working in the Banach space setting, F. Sukochev and his coauthors extended this relationship to a one- to- one correspondence between all continuous traces t on A( H) and all continuous symmetric linear forms. on a( N). Combining this result with [ 4, Corollary 5.6] yields some kind of trace formulas: