Ilijas Farah: Notes not (yet?) intended for publication

  1. On sigma-algebra of subsets of R^2 generated by rectangles, November 2010.
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    (Warning: If you are a set-theorist, then you will probably not learn much from this note.)
  2. Orthonormal bases in Hilbert spaces, August 2009.
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    The main result of this note has been known. See
    Orthonormal bases and quasi-splitting subspaces in pre-Hilbert spaces D. Buhagiar, E. Chetcuti, H. Weber, J. Math. Anal. Appl., 345 (2008) 725-730.
    and the references thereof. Thanks to Nigel Kalton to pointing this out.
  3. Some problems about operator algebras with set-theoretic flavor,
    For the time being I gave up on trying to maintain a list of problems. Many of the problems have been solved in a short period of time, most notably the Kadison-Singer problem and Arveson's problem on whether every operator system has sufficiently many boundary representations? You may still want to check the list of problems from AIM Set theory and C*-algebras site,
    but check whether the problem that you intend to work on has been solved already.
  4. Addendum to "All automorphisms of the Calkin algebra are inner", July 2007. (This is an addendum to earlier (prior to July 2007) versions of All automorphisms of the Calkin algebra are inner; it has been included in the revised version of this paper.)
    dvi file postscript file pdf file
  5. A simple construction of an outer automorphism of the Calkin algebra using the Continuum Hypothesis, February 2007 (now included in `All automorphisms of the Calkin algebra are trivial`).
    postscript file dvi file pdf file
  6. A twist of projections in the Calkin algebra, October 2006.
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  7. C* algebras and their representations , February 2006, slightly updated October 2006.
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  8. Woodin's proof that NS saturated almost implies CH fails , October 2005.
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  9. Convolutions of pathological submeasures, April 2005.
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  10. Another characterization of nonmeager ideals, February 2003.
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  11. Maximal measure algebras in P(N)/Z_0, October 2002.
    postscript file dvi file pdf file
  12. A saturated ideal and Sigma-2-1 absoluteness: renamed to `A proof of the Sigma-2-1 absoluteness theorem' and moved to preprints.
  13. Continuum Hypothesis implies Aut(P(N)/Z) is simple, June 1999 (included in Analytic quotients)
    postscript file dvi file pdf file
  14. Every compactum that maps onto its own square maps onto its own countable infinite product, (now included in `Powers of N*')
    postscript file dvi file pdf file
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