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Extension of Operator Lipschitz and Commutator Bounded Functions.

Authors :
Gohberg, I.
Alpay, D.
Arazy, J.
Atzmon, A.
Ball, J. A.
Ben-Artzi, A.
Bercovici, H.
Böttcher, A.
Clancey, K.
Coburn, L. A.
Curto, R. E.
Davidson, K. R.
Douglas, R. G.
Dijksma, A.
Dym, H.
Fuhrmann, P. A.
Gramsch, B.
Helton, J. A.
Kaashoek, M. A.
Kaper, H. G.
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