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On the spectrum of C 1 as an operator on bv 0 . (English) Zbl 0691.40004
Summary: J. Reade [Bull. Lond. Math. Soc. 17, 263-267 (1985; Zbl 0548.47017)] determined the spectrum of C 1 regarded as an operator on the space c 0 of all null sequences normed by x=sup n0 |x n |· It is the purpose of this paper to determine the spectrum of C 1 regarded as an operator on the space bv 0 of all sequences x such that x k 0 as k and x= k=0 |x k+1 -x k |<·

MSC:
40F05Absolute and strong summability
47A10Spectrum and resolvent of linear operators