In this paper, subnormal operators, not necessarily bounded, are discussed as generalized observables. In order to describe not only the information about the probability distribution of the output data of their measurement but also a framework of their implementations, we introduce a new concept compound-systemtype normal extension, and we derive the compound-system-type normal extension of a ...

The trend of progressive opinion concerning the hospital care of the mentally subnormal is well expressed in a Ministry of Health Memorandum [(65)104] on Improving the Effectiveness of the Hospital Service for the Mentally Subnormal. It states: "In the absence of complicating conditions, such as severe physical disability or disturbed behaviour, the severely subnormal patient who has been adequ...

Let B1 and B2 be disjoint separable algebraic extensions of a field F, and let B = B1B2 be their composite. Let α1 be an element of B1 and α2 be an element of B2. Suppose α1 and α2 are primitive (resp. normal, resp. subnormal). We investigate the question of when α1 +α2 and α1α2 are necessarily primitive (resp. normal, resp. subnormal) elements of B. (A normal element of a Galois extension is d...

Abstract. We study the Subnormal Completion Problem (SCP) for 2-variable weighted shifts. We use tools and techniques from the theory of truncated moment problems to give a general strategy to solve SCP. We then show that when all quadratic moments are known (equivalently, when the initial segment of weights consists of five independent data points), the natural necessary conditions for the exi...