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Extension of Operator Lipschitz and Commutator Bounded Functions.
- Source :
- Extended Field of Operator Theory; 2007, p225-244, 20p
- Publication Year :
- 2007
-
Abstract
- Let (B(H) ‖·‖) be the algebra of all bounded operators on an infinite-dimensional Hilbert space H. Let B(H)sa be the set of all selfadjoint operators in B(H). Throughout the paper we denote by α a compact subset of ℝ and by B(H)sa(α) the set of all operators in B(H)sa with spectrum in α: $$ B(H)_{sa} (\alpha ) = \{ A = A^* \in B(H): Sp(A) \subseteq \alpha \} . $$ We will use similar notations Asa, Asa(α) for a Banach *-algebra A. Each bounded Borel function g on α defines, via the spectral theorem, a map A → g(A) from B(H)sa(α) into B(H). Various smoothness conditions when imposed on this map define the corresponding classes of operator-smooth functions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISBNs :
- 9783764379797
- Database :
- Supplemental Index
- Journal :
- Extended Field of Operator Theory
- Publication Type :
- Book
- Accession number :
- 33097717
- Full Text :
- https://doi.org/10.1007/978-3-7643-7980-3_11