A GENERALIZATION OF THE 0-NUMERICAL RANGE
Let H be a complex Hilbert space. Given a bounded linear operator A on H, we describe the set R n (A) = fV AW : V;W : C n ! H;V V = W W = In;V W = 0g. It is shown that the closed matricial convex hull of R n (A) is a closed ball of radius minfkA I k : 2 Cg centered at the origin.
Wigner's theorem in Hilbert C^*-modules over C^*-algebras of compact operators
Let W be a Hilbert C ⁄ -module over the C ⁄ - algebra A 6 C of all compact operators on a Hilbert space. It is proved that any function T : W ! W which pre- serves the absolute value of the A-valued inner product is of the form Tv = '(v)Uv; v 2 W, where ' is a phase func- tion and U is an A-linear isometry. The result generalizes Molnar's extension of Wigner's classical unitary-antiunitary theorem.
Rapid Spatially Coupled AVO Inversion
The Bayesian methodology yields a natural framework for many geophysical inverse problem, see e.g. (Tarantola and Valette, 1982; Tarantola, 1987; Duijndam, 1988a; Duijndam, 1988b). The solution of a Bayesian inverse problem is represented by the posterior distribution. From the posterior distribution the best estimate and the corresponding uncertainty can be extracted and a set of plausible solutions can be drawn.