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Generalized slant Toeplitz operators on H 2
Author(s) -
Arora S. C.,
Batra Ruchika
Publication year - 2005
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/mana.200310244
Subject(s) - mathematics , toeplitz matrix , invertible matrix , unit circle , spectral radius , toeplitz operator , eigenvalues and eigenvectors , complex plane , operator (biology) , spectrum (functional analysis) , hardy space , combinatorics , order (exchange) , algebraic number , product (mathematics) , radius , pure mathematics , integer (computer science) , mathematical analysis , geometry , physics , quantum mechanics , computer security , repressor , chemistry , computer science , biochemistry , transcription factor , programming language , finance , economics , gene
For an integer k ≥ 2, k th ‐order slant Toeplitz operator U φ [1] with symbol φ in L ∞ (), where is the unit circle in the complex plane, is an operator whose representing matrix M = ( α ij ) is given by α ij = 〈 φ , z ki–j 〉, where 〈. , .〉 is the usual inner product in L 2 (). The operator V φ denotes the compression of U φ to H 2 () (Hardy space). Algebraic and spectral properties of the operator V φ are discussed. It is proved that spectral radius of V φ equals the spectral radius of U φ , if φ is analytic or co‐analytic, and if T φ is invertible then the spectrum of V φ contains a closed disc and the interior of the disc consists of eigenvalues of infinite multiplicities. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)