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Let A denote the class of bounded linear Hilbert space
operators with the property that jA2j ¸ jAj2. In this paper we
show that A-operators are ¯nitely ascensive and that, for non-zero
operators A and B, A B is in A if and only if A and B are in
A. Also, it is shown that if A is an operator such that p(A) is in
A for a non-trivial polynomial p, then Weyl's theorem holds for
f(A), where f is a function analytic on an open neighborhood of
the spectrum of A.
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