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General orthogonal systems of coordinates in the separable and complete Hilbert-Hermite-space

  • Otton Martin Nikodým
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 129)

Abstract

One of the advantages of the theory of summation, [R I.], is the possibility of defining a system of coordinates (in H.-H.-space), which is more general, than the usual one, composed of a saturated system of mutually orthogonal and normed vectors \(\{{{\overrightarrow{\varphi }}_{n}}\},\) n = 1, 2, ... The usual, just mentioned system of coordinates, is well adapted to the discontinuous spectrum of a normal operator, but it does not work well in the case of a continuous spectrum. The theory, which we are going to sketch, is completely general: it covers in a unified way both possibilities of spectrum.

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Copyright information

© Springer-Verlag New York Inc. 1966

Authors and Affiliations

  • Otton Martin Nikodým
    • 1
  1. 1.UticaUSA

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