Complex dynamical systems and the geometry of domains in Banach spaces

Mark Elin; Simeon Reich; David Shoikhet

Displaying similar documents to “Complex dynamical systems and the geometry of domains in Banach spaces”

Generation theory for semigroups of holomorphic mappings in Banach spaces.

Reich, Simeon, Shoikhet, David (1996)

Abstract and Applied Analysis

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Semigroups and generators on convex domains with the hyperbolic metric

Simeon Reich, David Shoikhet (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let $D$ be domain in a complex Banach space $X$ , and let $ρ$ be a pseudometric assigned to $D$ by a Schwarz-Pick system. In the first section of the paper we establish several criteria for a mapping $f : D \to X$ to be a generator of a $ρ$ -nonexpansive semigroup on $D$ in terms of its nonlinear resolvent. In the second section we let $X = H$ be a complex Hilbert space, $D = B$ the open unit ball of $H$ , and $ρ$ the hyperbolic metric on $B$ . We introduce the notion of a $ρ$ -monotone mapping and obtain simple characterizations of...

Fully summing mappings between Banach spaces

Mário C. Matos, Daniel M. Pellegrino (2007)

Studia Mathematica

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We introduce and investigate the non-n-linear concept of fully summing mappings; if n = 1 this concept coincides with the notion of nonlinear absolutely summing mappings and in this sense this article unifies these two theories. We also introduce a non-n-linear definition of Hilbert-Schmidt mappings and sketch connections between this concept and fully summing mappings.