NEUE STRUKTURSÄTZE FÜR RIESZSCHE UND VERWANDTE RÄUME

Abstract

The so-called coordinatization problem of abstract spaces, due to D. Hilbert, O. Veblen and W. Young, has been solved about fifty years ago by means of modern algebraical methods in case of certain extensions of projective geometry by J. Neumann und I. Halperin, but it has been investigated quite recently by the author in another direction, name!y for the Riesz spaces LP and related classes of functions. (Cf. e.g. Abstract of Comm., ICM Helsinki, 1978 and ICM Berkeley, 1986.) - This paper is intended primarily to the following questions: in which sense can be transferred the Riesz - Fischer theorem on Hilbert spaces (which is as well- known of fundamental importance in the quantum theory, too) to more general function classes according to the above-mentioned aspects: further, what kinds of new type "structural theo- rems" ran be ohtained on this way.