Displaying similar documents to “Power-dominated elements in a Banach algebra”

Complexifications of real Banach spaces, polynomials and multilinear maps

Gustavo Muñoz, Yannis Sarantopoulos, Andrew Tonge (1999)

Studia Mathematica

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We give a unified treatment of procedures for complexifying real Banach spaces. These include several approaches used in the past. We obtain best possible results for comparison of the norms of real polynomials and multilinear mappings with the norms of their complex extensions. These estimates provide generalizations and show sharpness of previously obtained inequalities.

A resolvent condition implying power boundedness

Béla Nagy, Jaroslav Zemánek (1999)

Studia Mathematica

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The Ritt and Kreiss resolvent conditions are related to the behaviour of the powers and their various means. In particular, it is shown that the Ritt condition implies the power boundedness. This improves the Nevanlinna characterization of the sublinear decay of the differences of the consecutive powers in the Esterle-Katznelson-Tzafriri theorem, and actually characterizes the analytic Ritt condition by two geometric properties of the powers.