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Unitary Couplings, Scattering Suboperators and Regular Factorizations of Bounded Operator Valued Functions
Author(s) -
Boiko S.S.,
Dubovoy V.K.
Publication year - 2002
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200203)236:1<47::aid-mana47>3.0.co;2-c
Subject(s) - mathematics , unitary state , unitary operator , operator (biology) , factorization , generalization , pure mathematics , connection (principal bundle) , algebra over a field , bounded function , shift operator , discrete mathematics , mathematical analysis , compact operator , algorithm , hilbert space , computer science , extension (predicate logic) , biochemistry , chemistry , repressor , political science , transcription factor , law , gene , geometry , programming language
The purposes of this paper are to introduce the concept of a regular factorization for a contractive operator function of the class L ∞ and to develop methods connected with this concept. This approach proved to be rather fruitful in research of contractive operator functions. The apparatus constructed here is a generalization of the well‐known methods of the theory of unitary colligations and of their characteristic operator functions. In this connection, it turned out to be necessary to present some known facts of the theory of unitary couplings and of their scattering suboperators in a new form.