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Semigroups of Operators and Interpolation

Part of the Systems & Control: Foundations & Applications book series (SCFA)

Abstract

We shall denote by X a complex Banach space of norm | · |, and by \( \mathcal{L}{\text{(}}X{\text{)}} \) the Banach algebra of all linear continuous mappings T: XX. The linear space \( \mathcal{L}{\text{(}}X{\text{)}} \) is endowed with the usual norm: For any \( T \in \mathcal{L}{\text{(}}X{\text{)}} \)
$$ ||T||{\text{ = sup \{ |}}Tx|{\text{:}}x \in X,|x| \leqslant 1\} . $$
(1.1)

Keywords

Hilbert Space Banach Space Strong Solution Mild Solution Fractional Power 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 2007

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