By using the method of sub- and supersolutions, we study existence positive solutions for a class singular nonlinear semipositone systems involving nonlocal operators.

We study the positive-operator-valued measures on the projective real line covariant with respect to the projective group, assuming that the energy is a positive operator. This problem is similar to the more complicated problem of finding the positive-operator-valued measures on the compactified Minkowski space-time covariant with respect to the conformal group. It also describes a time-of-arri...

Let T be a quadratic operator on a complex Hilbert space H. We show that T can be written as a product of two positive contractions if and only if T is of the form aI ⊕ bI ⊕ ( aI P 0 bI ) on H1 ⊕H2 ⊕ (H3 ⊕H3) for some a, b ∈ [0, 1] and strictly positive operator P with ‖P‖ ≤ | √ a− √ b| √ (1− a)(1− b). Also, we give a necessary condition for a bounded linear operator T with operator matrix ( T1...