The Collaborative International Dictionary of English v.0.48:

established \established\ adj.
   1. brought about or set up or accepted; especially long and
      widely accepted; as, distrust of established authority; a
      team established as a member of a major league; enjoyed
      his prestige as an established writer; an established
      precedent; the established Church. Contrasted with
      unestablished. [Narrower terms: entrenched;
      implanted, planted, rooted; official; recognized]
      [WordNet 1.5]

   2. securely established; as, an established reputation.

   Syn: firm.
        [WordNet 1.5]

   3. settled securely and unconditionally.

   Syn: accomplished, effected.
        [WordNet 1.5]

   4. conforming with accepted standards.
      [WordNet 1.5]

   5. shown to be valid beyond a reasonable doubt; as, the
      established facts in the case.

   Syn: proved.
        [WordNet 1.5 +PJC]

   6. (Bot.) introduced from another region and persisting
      without cultivation; -- of plants.

   Syn: naturalized.
        [WordNet 1.5 +PJC]