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Hilbert compact

Last-modified: 2010-08-24 (火) 14:35:53

Definition Edit

  • Let H be a Hilbert space. An absolutely convex compact C ⊂ H is called a Hilbert compact in H if the space imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20H_C=%5cmbox%7bSpan%7d%5c%20C%20%5c%5d%7d%25.png equipped with the Banach norm imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5c%7c%5ccdot%5c%7c_C%20%5c%5d%7d%25.png generated by C is isomorphic to a Hilbert space and dense in H.

Reference Edit

  • I. V. Orlov, Hilbert compacts, compact ellipsoids, and compact extrema, Journal of Mathematical Sciences, Vol. 164, No. 4, 2010