Business associations in government ownership attend to significant public duties. Their activities, the quality, efficiency and fruitfulness of their business management have a considerable impact on the quality of life, security, health and welfare of the population using their services and contribute to the responsible management of public funds. In other words, the reasonable, compliant and effective operation of businesses operating in public interest is one of the most important social objectives. The State Audit Office's contribution includes its audits, analyses, studies, consultancy to management systems, performed on the basis of the Hungarian National Assembly's authorisation given in a resolution, and its support to training executives in the field of public finances. The article presents their valuegenerating utilisation.

In 1972 V. I. Lomonosov discovered a technique which settled the longstanding problem of whether or not two commutative compact operators have a common invariant subspace. He actually proved more: If A is a compact operator, then A shares a common invariant subspace with every operator that commutes with it. In fact as he asserted, a slight modification of his proof shows that the conclusion holds if A merely commutes with a compact operator. His technique, which utilizes the Schauder fixed point theorem, was immediately seized upon by many people and used to produce even stronger invariant subspace theorems. The paper A survey of the Lomonosov technique in the theory of invariant subspaces, by C. Pearcy and Allen L. Shields takes us through Lomonosov's contribution to some of its consequences and also discusses the current interesting state of the invariant subspace problem. A goodly portion of this material has also appeared in the monograph Invariant subspaces of H. Radjavi and P. Rosenthal, Springer-Verlag, Berlin, 1973. There is much of interest in this book. The writing is generally brisk and meets a high standard for mathematical exposition. These essays can contribute a great deal to showing students some of the areas of operator theory that have been and are still the subject of considerable research.