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Algebraic Aspects of the Paving and Feichtinger Conjectures

  • Eric Weber
Part of the Operator Theory: Advances and Applications book series (OT, volume 202)

Abstract

The Paving Conjecture in operator theory and the Feichtinger Conjecture in frame theory are both problems that are equivalent to the Kadison-Singer problem concerning extensions of pure states. In all three problems, one of the difficulties is that the natural multiplicative structure appears to be incompatible — the unique extension problem of Kadison-Singer is compatible with a linear subspace, but not a subalgebra; likewise, the pavable operators is known to be a linear subspace but not a subalgebra; the Feichtinger Conjecture does not even have a linear structure. The Paving Conjecture and the Feichtinger Conjecture both have special cases in terms of exponentials in L2[0, 1]. We introduce convolution as a multiplication to demonstrate a possible attack for these special cases.

Keywords

Kadison-Singer Problem Paving Laurent operator frame 

Mathematics Subject Classification (2000)

Primary: 46L99 Secondary 46B99 42B35 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  • Eric Weber
    • 1
  1. 1.Department of MathematicsIowa State UniversityAmesUSA

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