Support of a joint resolution of identity and the projection spectral theorem

Pulemyotov, Artem D. (2003) Support of a joint resolution of identity and the projection spectral theorem. Infinite Dimensional Analysis Quantum Probability and Related Topics, 6 4: 549-561. doi:10.1142/S0219025703001444


Author Pulemyotov, Artem D.
Title Support of a joint resolution of identity and the projection spectral theorem
Journal name Infinite Dimensional Analysis Quantum Probability and Related Topics   Check publisher's open access policy
ISSN 0219-0257
Publication date 2003-12
Sub-type Article (original research)
DOI 10.1142/S0219025703001444
Volume 6
Issue 4
Start page 549
End page 561
Total pages 13
Place of publication Singapore, Singapore
Publisher World Scientific Publishing
Collection year 2003
Language eng
Formatted abstract
Let A = (Ax)x2X be a family of commuting normal operators in a separable Hilbert
space H0. Obtaining the spectral expansion of A involves constructing of the corre-
sponding joint resolution of identity E. The support supp E is not, in general, a set of
full measure. This causes numerous diffiulties, in particular, when proving the projec-
tion spectral theorem, i.e. the main theorem about the expansion in generalized joint
eigenvectors. In this work, we show that supp E has a full outer measure under the
conditions of the projection spectral theorem. Using this result, we simplify the proof of
the theorem and rene its assertions.
Keyword Spectral theorem
Joint resolution of identity
Generalized eigenvector
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Created: Thu, 18 Oct 2012, 16:43:31 EST by Kay Mackie on behalf of School of Mathematics & Physics