Periodica Mathematica Hungarica

, Volume 13, Issue 4, pp 273–287 | Cite as

Spectral measures, II: Characterization of scalar operators

  • W. V. Smith
Article
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Revised:

Abstract

We continue the development of part I. The Riesz representation theorem is proved without assuming local convexity. This theorem is applied to give sufficient conditions for an operator (continuous or otherwise) to be “spectral”. A uniqueness problem is pointed out and the function calculus is extended to the case of several variables. A Radon—Nikodym theorem is proved.

AMS (MOS) subject classifications (1980)

Primary 47B40 Secondary 28B05, 46A15, 46H05 

Key words and phrases

Topological vector space Riesz theorem spectral measures 
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Copyright information

© Akadémiai Kiadó 1982

Authors and Affiliations

  • W. V. Smith
    • 1
  1. 1.Mathematics DepartmentUniversity of MississippiMississippiUSA

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