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Results on Spectral Measures and an Application to a Spectral Theorem
Department of Mathematics, University of Texas, Edinburg, TX, USA
- 1 Department of Mathematics, University of Texas, Edinburg, TX, USA
Advances in Pure Mathematics·Volume 15 (2025)·Pages 339–349·Published 23 May 2025·DOI10.4236/apm.2025.155017
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Abstract
Properties of Hilbert spaces, projections and spectral measures are introduced and studied. Spectral integrals and the related operator are considered, and their relationship with the spectrum of an operator is given. The theorems that result yield a version of the spectral theorem which is suited to infinite dimensions.
KeywordsProjectionAdjointHilbert SpaceSpectral MeasureOperatorSpectrumIdempotent
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