A Family of Almost Invertible Infinite Matrices

Abstract

An algebraic analogue of the family of Fredholm operators is introduced for the family of row and column finite matrices, dubbed "Fredholm matrices." In addition, a measure is introduced which indicates how far a Fredholm matrix is from an invertible matrix. It is further shown that this measure respects multiplication, is invariant under perturbation by a matrix from $M_{\infty }(K)$, and is invariant under conjugation by an invertible row and column finite matrix.

8 Pages