Abstract We prove an extension of the Moore–Schmidt theorem on triviality first cohomology class cocycles for action arbitrary discrete group measure space and with values in compact Hausdorff abelian group. The proof relies a ‘conditional’ Pontryagin duality spaces abstract measurable maps.

a literature review revealed that most of the empirical equations introduced for determination of the uniaxial compressive strength (ucs) of rocks based on the schmidt hammer rebound number (n) are not sufficiently reliable mostly due to the relatively low coefficient of correlations. this is attributed to the fact that in most cases one formula is used for all types of rocks, although...

The operator-Schmidt decomposition is useful in quantum information theory for quantifying the nonlocality of bipartite unitary operations. We construct a family of unitary operators on C ⊗ C whose operatorSchmidt decompositions are computed using the discrete Fourier transform. As a corollary, we produce unitaries on C ⊗ C with operatorSchmidt number S for every S ∈ {1, ..., 9}. This corollary...

In this paper we deal with the connection of frames with the class of Hilbert Schmidt operators. First we give an easy criteria for operators being in this class using frames. It is the equivalent to the criteria using orthonormal bases. Then we construct Bessel sequences frames and Riesz bases for the class of Hilbert Schmidt operators using the tensor product of such sequences in the original...