Premium
Norms of Powers in Banach Algebras
Author(s) -
Pedersen Thomas Vils
Publication year - 1995
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/blms/27.4.305
Subject(s) - mathematics , banach space , bounded function , banach algebra , power series , pure mathematics , absolute convergence , operator (biology) , discrete mathematics , mathematical analysis , fourier series , biochemistry , chemistry , repressor , transcription factor , gene
By showing the existence of certain functions in A + (the algebra of analytic functions in the unit disc with absolutely convergent Taylor series), we prove that if T is a power bounded operator on a Banach space X , and x ∈ X satisfies Tx ≠ x , then∑ n − 1 ∞‖( 1 − T ) n x ‖‖( 1 − T )n − 1 x ‖ diverges .