A non-hyponormal operator generating Stieltjes moment sequences

A linear operator $S$ in a complex Hilbert space \hh for which the set \dzn{S} of its $C^\infty$-vectors is dense in \hh and $\{\|S^n f\|^2\}_{n=0}^\infty$ is a Stieltjes moment sequence for every f \in \dzn{S} is said to generate Stieltjes moment sequences. It is shown that there exists a closed non-hyponormal operator $S$ which generates Stieltjes moment sequences. What is more, \dzn{S} is a core of any power $S^n$ of $S$. This is established with the help of a weighted shift on a directed tree with one branching vertex. The main tool in the construction comes from the theory of indeterminate Stieltjes moment sequences. As a consequence, it is shown that there exists a non-hyponormal composition operator in an $L^2$-space (over a $\sigma$-finite measure space) which is injective, paranormal and which generates Stieltjes moment sequences. In contrast to the case of abstract Hilbert space operators, composition operators which are formally normal and which generate Stieltjes moment sequences are always subnormal (in fact normal). The independence assertion of Barry Simon's theorem which parameterizes von Neumann extensions of a closed real symmetric operator with deficiency indices $(1,1)$ is shown to be false

Direct comparison of the performance of CZT detectors contacted with various metals

Cadmium Zinc Telluride (CZT) achieves excellent spatial resolution and good energy resolution over the broad energy range from several keV into the MeV energy range. In this paper we present the results of a systematic study of the performance of CZT detectors manufacturered by Orbotech (before IMARAD) depending on surface preparation, contact materials and contact deposition. The standard Orbotech detectors have the dimension of 2.0 x 2.0 x 0.5 cm. They have a pixellated In anode with 8 x 8 pixels and a monolithic In cathode. Using the same CZT substrates several times, we have made a direct comparison of the performance of different contact materials by replacing the cathode and/or the anode contacts with several high-workfunction metals. We present the performance of the detectors and conclude with an overview over our ongoing detector optimization.Comment: 8 pages, 5 figures, to appear in the proceedings of the conference 5922, "Hard X-Ray and Gamma-Ray Detector Physics VII" on the "Optics & Photonics 2005" SPIE Symposium, July 31- August 4, 2005, San Diego, C