LINEAR MAPS PRESERVING REGULARITY IN C~*-ALGEBRAS

摘要

Let A and B be unital C~*-algebras such that at least one of them is of real rank zero. We investigate surjective linear maps from A to B preserving the conorm, the (von Neumann) regularity, the generalized spectrum, and their essential versions. As a consequence, we recover results of Mbekhta, and Mbekhta and Semrl for L(H) when H is an infinite-dimensional complex Hilbert space.