@inbook{43f39f1439e349a1ba62527ef638bddc,

title = "Q-functions of Quasi-selfadjoint Contractions",

abstract = "A bounded everywhere defined operator T in a Hilbert space H is said to be a quasi-selfadjoint contraction or (for short) a qsc-operator, if T is a contraction and ker (T − T*) ≠ {0}. For a closed linear subspace N of H containing ran (T − T*) the operator-valued function QT(z) = PN(T − zI)^−1↾N, |z| > 1, where PN is the orthogonal projector from H onto N, is said to be a Q-function of T acting on the subspace N. The main properties of such Q-functions are studied, in particular the underlying operator-theoretical aspects are considered by using some block representations of the contraction T and analytical characterizations for such functions QT(z) are established. Also a reproducing kernel space model for QT(z) is constructed. In the special case where T is selfadjoint QT(z) coincides with the Q-function of the symmetric operator A := T↾(H ⊖ N) and its selfadjoint extension T = T* in the usual sense.",

keywords = "resolvent, operator model, Q-function, quasi-selfadjoint operator, contractive extension, symmetric contraction",

author = "Arlinskiĭ, {Yury M.} and Seppo Hassi and {de Snoo}, Henk",

note = "Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen, Research Institute for Mathematics and Computing Science (IWI)",

year = "2005",

doi = "10.1007/3-7643-7516-7_2",

language = "English",

isbn = "978-3-7643-7515-7",

volume = "163",

series = "Operator Theory: Advances and Applications",

publisher = "University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science",

pages = "23--54",

booktitle = "Operator Theory and Indefinite Inner Product Spaces",

}