Cwikel's bound is extended to an operator-valued setting. One application of this result is a semi-classical bound for the number of negative bound states for Schrödinger operators with operator-valued potentials. We recover Cwikel's bound for the Lieb-Thirring constant L0,3 which is far worse than the best available by Lieb (for scalar potentials). However, it leads to a uniform bound (in the dimension d≥3) for the quotient L0,d/Lcl0,d is the so-called classical constant. This gives some improvement in large dimensions.
"On the number of bound states for Schrödinger operators with operator-valued potentials." Ark. Mat. 40 (1) 73 - 87, April 2002. https://doi.org/10.1007/BF02384503