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Norms of Inverses and Pseudospectra

  • Albrecht Böttcher
  • Bernd Silbermann
Chapter
  • 596 Downloads
Part of the Universitext book series (UTX)

Abstract

C*-algebras are especially nice Banach algebras. A map \( a \mapsto {a^*} \) of a Banach algebra A onto itself is called an involution if
$$ {a^{**}} = a,{\left( {a + b} \right)^*},{\left( {ab} \right)^*} = {b^*}{a^*},{\left( {\lambda a} \right)^*} = \mathop \lambda \limits^ -{a^*} $$
for all a, b ∈ A and all.λ ∈ C. A C*-algebra is a Banach algebra with an involution such that
$$ \left\| {aa^* } \right\| = \left\| a \right\|^2 {\rm{ for all }}a \in A. $$
(3.1)

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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Albrecht Böttcher
    • 1
  • Bernd Silbermann
    • 1
  1. 1.Fakultät für MathematikTechnische Universität ChemnitzChemnitzGermany

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