Self-stabilization in certain infinite-dimensional matrix algebras

Abstract

Analytical tools to $K$-theory; namely, self-stabilization of rapidly decreasing matrices, linearization of cyclic loops, and the contractibility of the pointed stable Toeplitz algebra are discussed in terms of concrete formulas. Adaptation to the *-algebra and finite perturbation categories is also considered. Moreover, the finite linearizability of algebraically finite cyclic loops is demonstrated.