Recently, Jensen [3], Lazar [4] and Rothwell [6] have investigated in detail the structure of scattered C*-algebras which can be regarded as the most elementary generalization of the finite dimensional involutive algebras. A C*-algebra si is called scattered if every positive functional of si is the sum of a sequence of pure functionals. The object of this note is to give a short proof of a nat...

1. J. Burbea, Sharp inequalities for holomorphic functions, Illinois J. Math. 31 (1987) 248–264. 2. T. Carleman, Zur Theorie der Minimalflächen, Math. Z. 9 (1921) 154–160. 3. P. L. Duren, Theory of H p Spaces, Academic Press, New York, 1970; reprinted by Dover, Mineola, NY, 2000. 4. T. W. Gamelin and D. Khavinson, The isoperimetric inequality and rational approximation, this MONTHLY 96 (1989) 1...

Contents Chapter 1. Martingales, continued 1 1.1. Martingales indexed by partially ordered sets 1 1.2. Notions of convergence for martingales 3 1.3. Uniform integrability 4 1.4. Convergence of martingales with directed index sets 6 1.5. Application: The 0-1 law of Kolmogorov 8 1.6. Continuous-time martingales 9 1.7. Tail bounds for martingales 12 1.8. Application: The Pólya urn 13 1.9. Applicat...

As particular case of the Radon-Nikodym theorem we show that any count distribution is a weighted Poisson distribution (WPD) and, more generally, a weighted version of any other count distribution with suitable support. Several properties and consequences of this result are then given. With a condition on their supports, we deduce that two count distributions are connected by the weightening op...

Dosiev (2008) obtained a Stinespring’s theorem for local completely positive maps (in short: CP-maps) on locally C ∗ -algebras. In this article suitable notion of minimality construction has been identified so as to ensure uniqueness up unitary equivalence the associated representation. Using Radon–Nikodym type proved. Further, unbounded operator valued Hilbert modules over -algebras (also call...