The spectrum of the Cesàro operator on c0(c0)
| dc.contributor.author | Okutoyi, J. I. | |
| dc.contributor.author | Thorpe, B. | |
| dc.date.accessioned | 2014-05-27T09:17:51Z | |
| dc.date.available | 2014-05-27T09:17:51Z | |
| dc.date.issued | 1989-01 | |
| dc.description | DOI: http://dx.doi.org/10.1017/S0305004100001420 | en_US |
| dc.description.abstract | In a recent paper [6], the spectrum of the Cesàro operator C on c0 (the space of null sequences of complex numbers with the sup norm) was obtained by finding the eigenvalues of the adjoinoperator on and showing that the operator (C–λI)−1 lies in B(c0) for all λ outside the closure of this set of eigenvalues. In this paper we apply a similar method to find the spectrum of the two-dimensional Cesàro operator on a space of double sequences c0(c0) (defined in §2). We shall introduce a simplification to the proof in [6] by observing that (C – λI)−1, when it exists, is a Hausdorff summability method (see page 288 of [11] for the single variable case on the space of convergent sequences c), and the crux of our proof is to show that the moment constant associated with the method (C – λI)−1 is regular for the space c0(c0) and the set of λ under consideration. It turns out that c0(c0) c0 c0 (see page 237 of [7]) and that the two-dimensional Cesàro operator on c0(c0) is the tensor product C C of the Cesàro operator C on c0. Thus our result gives a direct proof that the spectrum σ(C C) equals σ(C)σ(C), which is a special case of the result of Schechter in [8]. | en_US |
| dc.identifier.citation | Mathematical Proceedings of the Cambridge Philosophical Society / Volume 105 / Issue 01 / January 1989, pp 123-129 | en_US |
| dc.identifier.issn | 0305-0041 | |
| dc.identifier.other | 1469-8064 | |
| dc.identifier.uri | http://ir-library.ku.ac.ke/handle/123456789/9643 | |
| dc.language.iso | en | en_US |
| dc.publisher | Cambridge University Press | en_US |
| dc.title | The spectrum of the Cesàro operator on c0(c0) | en_US |
| dc.type | Article | en_US |
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