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Boundary of polyhedral spaces: an alternative proof.

Libor Vesely (2000)

Extracta Mathematicae

A Banach space X is called polyhedral if the unit ball of each one of its finite-dimensional (equivalently: two-dimensional [6]) subspaces is a polytope. Polyhedral spaces were studied by various authors; most of the structural results are due to V. Fonf. We refer the reader to the surveys [1], [2] for other definitions of polyhedrality, main properties and bibliography. In this paper we present a short alternative proof of the basic result on the structure of the unit ball of the polyhedral space...

Boundary values of analytic semigroups and associated norm estimates

Isabelle Chalendar, Jean Esterle, Jonathan R. Partington (2010)

Banach Center Publications

The theory of quasimultipliers in Banach algebras is developed in order to provide a mechanism for defining the boundary values of analytic semigroups on a sector in the complex plane. Then, some methods are presented for deriving lower estimates for operators defined in terms of quasinilpotent semigroups using techniques from the theory of complex analysis.

Bounded analytic sets in Banach spaces

Volker Aurich (1986)

Annales de l'institut Fourier

Conditions are given which enable or disable a complex space X to be mapped biholomorphically onto a bounded closed analytic subset of a Banach space. They involve on the one hand the Radon-Nikodym property and on the other hand the completeness of the Caratheodory metric of X .

Bounded and unbounded operators between Köthe spaces

P. B. Djakov, M. S. Ramanujan (2002)

Studia Mathematica

We study in terms of corresponding Köthe matrices when every continuous linear operator between two Köthe spaces is bounded, the consequences of the existence of unbounded continuous linear operators, and related topics.

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