Linear maps preserving pseudospectrum and condition spectrum

We discuss properties of pseudospectrum and condition spectrum of an element in a complex unital Banach algebra and its -perturbation. Several results are proved about linear maps preserving pseudospectrum/ condition spectrum. These include the following: (1) Let A, B be complex unital Banach algebras and  > 0. Let : A  B be an -pseudospectrum preserving linear onto map. Then  preserves spectrum. If A and B are uniform algebras, then,  is an isometric isomorphism. (2) Let A, B be uniform algebras and 0 <  < 1. Let : A  B be an -condition spectrum preserving linear map. Then  is an -almost multiplicative map, where ,  tend to zero simultaneously.