Premium
Some applications of Banach algebra techniques
Author(s) -
Karaev M.,
Gürdal M.,
Saltan S.
Publication year - 2011
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.200910129
Subject(s) - mathematics , banach algebra , lp space , pure mathematics , approximation property , eigenvalues and eigenvectors , banach space , algebra over a field , convolution (computer science) , spectrum (functional analysis) , characterization (materials science) , product (mathematics) , finite rank operator , physics , materials science , geometry , quantum mechanics , machine learning , artificial neural network , computer science , nanotechnology
We consider some functional Banach algebras with multiplications as the usual convolution product * and the so‐called Duhamel product ⊛. We study the structure of generators of the Banach algebras ( C ( n ) [0, 1], *) and ( C ( n ) [0, 1], ⊛). We also use the Banach algebra techniques in the calculation of spectral multiplicities and extended eigenvectors of some operators. Moreover, we give in terms of extended eigenvectors a new characterization of a special class of composition operators acting in the Lebesgue space L p [0, 1] by the formula ( C φ f )( x ) = f (φ( x )).