Vol. 40, No. 2, 1972

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On the spectral radius formula in Banach algebras

Jan-Erik Björk

Vol. 40 (1972), No. 2, 279–284
Abstract

B will always denote a commutative semi-simple Banach algebra with a unit element. If f B then r(f) denotes its spectral radius. A sequence F = (fj)1 is called a spectral null sequence if fj1 for each j, while limj→∞r(fj) = 0. If F = (fj) is a spectral null sequence we put rN(F) = limsupj→∞fJN1∕N for each N 1. Finally we define the complex number rN(B) = sup{rN (F) : F is a spectral null sequence in B}. In general rN(B) = 1 for all N 1 and the aim of this paper is to study the case when rN(B) < 1 for some N.

Mathematical Subject Classification 2000
Primary: 46J05
Milestones
Received: 1 April 1970
Revised: 11 August 1970
Published: 1 February 1972
Authors
Jan-Erik Björk