A solution to a Dirichlet problem for the complex Monge-Ampère operator is characterized as a minimizer of an energy functional. A mutual energy estimate and a generalization of Hölder's inequality is proved. A comparison is made with corresponding results in classical potential theory.
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We construct a hereditarily indecomposable Banach space with dual space isomorphic to$ℓ$_{1}. Every bounded linear operator on this space is expressible as λ$I$+$K$, with λ a scalar and$K$compact.
Angela AlbericoIstituto per le Applicazioni del Calcolo “M. Picone”, Sez. Napoli-C.N.R.Andrea CianchiDipartimento di Matematica e Applicazioni per l'Architettura, Università di Firenze