caa a22 4500 386385866 CHVBK 20180307112058.0 cr unu---uuuuu 161130e198901 xx s 000 0 eng 10.1017/S0305004100001420 doi S0305004100001420 pii (NATIONALLICENCE)cambridge-10.1017/S0305004100001420 The spectrum of the Cesàro operator on c0(c0) [Elektronische Daten] 1. 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 adjoint operator 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) c0c0 (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]. Copyright © Cambridge Philosophical Society 1989 Okutoyi J. Department of Mathematics, Kenyatta University College, Nairobi, Kenya Thorpe B. Department of Mathematics, University of Birmingham, Birmingham B15 2TT Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/1(1989-01), 123-129 0305-0041 105:1<123 1989 105 PSP https://doi.org/10.1017/S0305004100001420 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0305004100001420 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Okutoyi J. Department of Mathematics, Kenyatta University College, Nairobi, Kenya NATIONALLICENCE 700 1- Thorpe B. Department of Mathematics, University of Birmingham, Birmingham B15 2TT NATIONALLICENCE 773 0- Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/1(1989-01), 123-129 0305-0041 105:1<123 1989 105 PSP CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge