On (A;m)-expansive operators

Abstract

We give several conditions for (A,m)-expansive operators to have the single-valued extension property. We also provide some spectral properties of such operators. Moreover, we prove that the A-covariance of any (A,2)-expansive operator T ∈ L(H) is positive, showing that there exists a reducing subspaceMon which T is (A,2)-isometric. In addition, we verify that Weyl's theorem holds for an operator T ∈L(H) provided that T is (T T; 2)-expansive. We next study (A,m)-isometric operators as a special case of (A,m)-expansive operators. Finally, we prove that every operator T ∈ L(H) which is (T T; 2)-isometric has a scalar extension. © Instytut Matematyczny PAN, 2012.