2022/07/17 by David de Hevia, de Hevia, David, Pedro Tradacete +1 · 2 citations
Mathematics · #46B42 #47A25 #47B91 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.2207.08090
openalex publication_date 2022/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 FBL\mathbb C[E] containing a linear isometric copy of E and satisfying the following universal property: for every complex Banach lattice X\mathbb C, every operator T:E→ X\mathbb C admits a unique lattice homomorphic extension T:FBL\mathbb C[E]→ X\mathbb C with ‖T‖=‖T‖. The free complex Banach lattice FBL\mathbb C[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 FBL\mathbb C[E] and FBL\mathbb C[F] are lattice isometric. The spectral theory of induced lattice homomorphisms on FBL\mathbb C[E] is also explored.