Open AccessThe compression of a slant Hankel operator to H2
Author(s) -
Taddesse Zegeye,
S. C. Arora
Publication year - 2003
Publication title -
publications de l'institut mathématique
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.246
H-Index - 17
eISSN - 1820-7405
pISSN - 0350-1302
DOI - 10.2298/pim0374129z
Subject(s) - unit circle , operator (biology) , hankel matrix , mathematics , compression (physics) , shift operator , isometry (riemannian geometry) , product (mathematics) , complex plane , combinatorics , mathematical analysis , pure mathematics , compact operator , physics , geometry , computer science , chemistry , biochemistry , repressor , transcription factor , extension (predicate logic) , gene , programming language , thermodynamics
A slant Hankel operator K? with symbol ? in L?(T) (in short L?), where T is the unit circle on the complex plane, is an operator whose representing matrix M = (aij) is given by ai,j = (?,z-2i-j), where (?, ?) is the usual inner product in L2(T) (in short L2). The operator L? denotes the compression of K? to H2(T) (in short H2). We prove that an operator L on H2 is the compression of a slant Hankel operator to H2 if and only if U *L = LU2, where U is the unilateral shift. Moreover, we show that a hyponormal L? is necessarily normal and L? can not be an isometry.