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Constructive Proof of Carpenter's Theorem

  Published:2013-11-13
 Printed: Sep 2014
  • Marcin Bownik,
    Department of Mathematics, University of Oregon, Eugene, OR 97403-1222, USA
  • John Jasper,
    Department of Mathematics, University of Missouri, Columbia, MO 65211-4100, USA
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Abstract

We give a constructive proof of Carpenter's Theorem due to Kadison. Unlike the original proof our approach also yields the real case of this theorem.
Keywords: diagonals of projections, the Schur-Horn theorem, the Pythagorean theorem, the Carpenter theorem, spectral theory diagonals of projections, the Schur-Horn theorem, the Pythagorean theorem, the Carpenter theorem, spectral theory
MSC Classifications: 42C15, 47B15, 46C05 show english descriptions General harmonic expansions, frames
Hermitian and normal operators (spectral measures, functional calculus, etc.)
Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
42C15 - General harmonic expansions, frames
47B15 - Hermitian and normal operators (spectral measures, functional calculus, etc.)
46C05 - Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
 

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