In this note we present necessary and sufficient conditions characterizing conditionally weakly compact sets in the space of (bounded linear) operator valued measures Mba(Σ,L(X,Y )). This generalizes a recent result of the author characterizing conditionally weakly compact subsets of the space of nuclear operator valued measures Mba(Σ,L1(X,Y )). This result has interesting applications in optim...

A new operator is considered, allowing compact formulae and proofs in the context of the derivation of a transfer matrix with respect to another matrix. The problem of the parametric sensitivity matrix calculation is chosen for illustration. It consists in deriving a Multiple Input Multiple Output transfer function with respect to a parametric matrix and is central in robust control theory. Eff...

We extend Lieb's limit theorem [which asserts that SO(3) quantum spins approach S classical spins as L-> oo] to general compact Lie groups. We also discuss the classical limit for various continuum systems. To control the compact group case, we discuss coherent states built up from a maximal weight vector in an irreducible representation and we prove that every bounded operator is an integral o...

The spectrum and degeneracies of the Dirac operator are analysed on compact coset spaces when there is a non-zero homogeneous background gauge field which is compatible with the symmetries of the space, in particular when the gauge field is derived from the spinconnection. It is shown how the degeneracy of the lowest Landau level in the recently proposed higher dimensional quantum Hall effect i...

We estimate the decay of correlations for some Markov maps on a countable states space. A necessary and suucient condition is given for the transfer operator to be quasi-compact on the space of locally Lipschitz functions. In the non quasi-compact case, the decay of correlations depends on the contribution to the transfer operator of the complementary of nitely many cylinders. Estimates are giv...