Banach 28

This lecture (banach28 ; don’t mind the tile) was given on 10/30/09



  1. def of L^\infty(T_\mu) given T_\mu and L^\infty(\mu)
  2. When two Borel measures are unitarily equivalent; \mu << \nu << \mu.  Question here.


  1. all op in L^\infty(T_\mu) (think its incorrect in notes) commute with T_\mu, T_mu^*.
  2. Cor. L^\infty(T_\mu) is max. abel. subalg of \mathscr{L}(L^2(\mu))
  3. Addendum: (???) a hilbert spac. op commutes also with T^*.
  4. The reducing subspace of T_\mu are the subspaces \chi_E(T_\mu)L^2(\mu) for E a Borel set.
  5. T_\mu \sim T_\nu iff \mu \sim \nu.  Here \sim means unitarily equivalent.

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