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Some Mapping Theorems for the Classes A n, m and the Boundary Sets
Author(s) -
Cassier G.,
Chalendar I.,
Chevreau B.
Publication year - 1999
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611599011892
Subject(s) - mathematics , extension (predicate logic) , mathematics subject classification , isometric exercise , unitary state , class (philosophy) , absolute continuity , boundary (topology) , contraction (grammar) , discrete mathematics , combinatorics , algebra over a field , pure mathematics , mathematical analysis , computer science , medicine , artificial intelligence , political science , law , programming language , physical therapy
Denote by A the class of all absolutely continuous contractions whose associated Sz. Nagy‐Foias functional calculus is isometric. Starting from the fact that if u is a non‐constant inner function and if T ∈ A, then so does u ( T ), we study how inner functions operate on the classes A n,m , subclasses of the class A. For this purpose, we use standard dual algebra techniques and a decomposition of the algebra H ∞ into a weak*‐topological direct sum of copies of itself. We also discuss mapping theorems for the support of the spectral measures associated with the unitary parts of the minimal isometric extension and the minimal co‐isometric extension of an absolutely continuous contraction T . 1991 Mathematics Subject Classification : primary 47D27; secondary 47A20, 47A15.