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 subspace M on 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.

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