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On the Approximation Numbers for the Finite Sections of Block Toeplitz Matrices
Author(s) -
Rogozhin A.,
Silbermann B.
Publication year - 2006
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609305018229
Subject(s) - toeplitz matrix , mathematics , fredholm determinant , block (permutation group theory) , operator (biology) , combinatorics , mathematics subject classification , matrix (chemical analysis) , function (biology) , pure mathematics , discrete mathematics , biochemistry , chemistry , materials science , repressor , evolutionary biology , biology , transcription factor , composite material , gene
In this paper we discuss the asymptotic distribution of the approximation numbers of the finite sections for a Toeplitz operator T ( a ) ∈ L ( l N p , μ) , 1 < p < ∞ and μ ∈ R, with a continuous matrix‐valued generating function a . We prove that the approximation numbers of the finite sections T n ( a ) = P n T ( a ) P n have the k ‐splitting property, provided T ( a ) is a Fredholm operator onl N p , μ. 2000 Mathematics Subject Classification 47B35 (primary), 15A18, 47A58, 47A75, 65F20 (secondary).