Abstract
The construction of the free Banach lattice generated by a real Banach space is extended to the complex setting. It is shown that for every complex Banach space E there is a complex Banach lattice FBLC[E] containing a linear isometric copy of E and satisfying the following universal property: for every complex Banach lattice XC, every operator T:E→XC admits a unique lattice homomorphic extension Tˆ:FBLC[E]→XC with ‖Tˆ‖=‖T‖. The free complex Banach lattice FBLC[E] is shown to have analogous properties to those of its real counterpart. However, examples of non-isomorphic complex Banach spaces E and F can be given so that FBLC[E] and FBLC[F] are lattice isometric. The spectral theory of induced lattice homomorphisms on FBLC[E] is also explored.
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