J Austral Math Soc Ser A 48 pp79--86, 1990.

On the Spectrum of C₁ as an Operator on bv₀

J. I. Okutoyi

Abstract

In 1985 John Reade determined the spectrum of C₁ regarded as an operator on the space c₀ of all null sequences normed by ||x|| = sup_{n ³ 0}|x_n|. It is the purpose of this paper to determine the spectrum of C₁ regarded as an operator on the space bv₀ of all sequences x such that x_k ® 0 as k ® ¥ and ||x|| = å^¥_k=0|x_k+1 - x_k| < ¥.

1980 AMS Subject Classification (1985 Revision): 40F05, 47A10

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Authors

J. I. Okutoyi

Kenyatta University, P.O.Box 43844, Nairobi, Kenya.