The Collaborative International Dictionary of English v.0.48:

Mesmerize \Mes"mer*ize\, v. t. [imp. & p. p. Mesmerized; p.
   pr. & vb. n. Mesmerizing.] [Also spelled mesmerise.]
   1. To bring into a state of mesmeric sleep; to hypnotize.
      [1913 Webster]

   2. To produce an intense fascination in; to spellbind.
      [PJC]

WordNet (r) 3.0 (2006):

mesmerized
    adj 1: having your attention fixated as though by a spell [syn:
           fascinated, hypnotized, hypnotised, mesmerized,
           mesmerised, spellbound, spell-bound, transfixed]