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Rosenthal-Banach compact

Last-modified: 2010-08-30 (月) 23:24:27

Definition Edit

  • A compact Hausdorff set K is called Rosenthal-Banach compact, if there is a polish space X and a Banach space E so that K is homeomorphic with a compact subset of B_1(X,E) in the topology of pointwise-weak convergence?, where B_1(X,E) is the set of functions which there is a sequence imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%28f_n%29_%7bn%5cin%5cmathbb%7bN%7d%7d%2c%5c%20f_n:X%5cto%28E%2c%5c%7c%5ccdot%5c%7c%29%20%5c%5d%7d%25.png continuous for every n ∈ N, such that if t ∈ X then imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5clim%20%5cmbox%7b%7d_%7bn%5cto%20p%7d%5c%7cf_n%28t%29-f%28t%29%5c%7c=0.%20%5c%5d%7d%25.png

Property Edit

Reference Edit

  • Mercourakis, S. and Stamati, E., Compactness in the first Baire class and Baire-1 operators. Serdica Math. J. 28 (2002), no. 1, 1--36.