Semigroups of Operators and Interpolation

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


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 \( T \in \mathcal{L}{\text{(}}X{\text{)}} \)
$$ ||T||{\text{ = sup \{ |}}Tx|{\text{:}}x \in X,|x| \leqslant 1\} . $$


Hilbert Space Banach Space Strong Solution Mild Solution Fractional Power 
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© Birkhäuser Boston 2007

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