It is proved that for V+=max(V,0) in the subspaee L1 (R+;L∞ (S1); r dr) of L1 (R2), there is a Cwikel-Lieb-Rosenblum-type inequality for the number of negative eigen-values of the operator ((1/i)∇+A)2-V in L2(R2) when A is an Aharonov-Bohm magnetic potential with non-integer flux. It is shown that the L1 (R+, L∞(S1), r dr)norm cannot be replaced by the L1 (R2)-norm in the inequality.
