Open AccessNonnegative unitary operators
Author(s) -
K.-H. Förster,
B. Nagy
Publication year - 2003
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-03-07202-2
Subject(s) - orthonormal basis , hilbert space , unitary state , mathematics , basis (linear algebra) , unitary operator , orthonormality , pure mathematics , operator (biology) , space (punctuation) , operator theory , set (abstract data type) , sequence (biology) , orthogonal basis , algebra over a field , computer science , geometry , physics , political science , transcription factor , repressor , law , chemistry , genetics , biology , operating system , biochemistry , quantum mechanics , programming language , gene
Unitary operators in Hilbert space map an orthonormal basis onto another. In this paper we study those that map an orthonormal basis onto itself. We show that a sequence of cardinal numbers is a complete set of unitary invariants for such an operator. We obtain a characterization of these operators in terms of their spectral properties. We show how much simpler the structure is in finite-dimensional space, and also describe the structure of certain isometries in Hilbert space.