Norms of Powers in Banach Algebras | Zendy

Pedersen Thomas Vils | Zendy

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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 .

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