Geodesic
Absolute Convexity in Spaces of Strongly Summable Sequences
Canadian mathematical bulletin, Tome 18 (1975) no. 1, pp. 67-75

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The space wp of strongly Cesàro summable sequences of index p > 0 has been investigated by several authors. In [2], Kuttner proved that no Toeplitz matrix could sum all sequences in wP, a result which was extended to coregular matrices by Maddox [5]. In [1], Borwein considered the continuous dual space of wp. The more general space w(p) has also been considered [3, 4], where p = (pk) is a strictly positive sequence. The r-convexity of the spaces w∞(p) and w0(p) was dealt with in a partial way in [8]. In the present note we establish criteria for the rconvexity of some general classes of [A, p]0 and [A, p]∞ spaces (see [6] and [7] for definitions), and in particular we give the necessary and sufficient conditions for the r-convexity of w∞(p) and w0(p). For most of the relevant definitions and notation we refer to [8]. 
Maddox, I. J.; Roles, J. W. Absolute Convexity in Spaces of Strongly Summable Sequences. Canadian mathematical bulletin, Tome 18 (1975) no. 1, pp. 67-75. doi: 10.4153/CMB-1975-013-7
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[1] 1. Borwein, D., Linear functionals connected with strong Cesaro summability, J. London Math. Soc, 40 (1965), 628-634. Google Scholar

[2] 2. Kuttner, B., Note on strong summability, J. London Math. Soc, 21 (1946), 118-122. Google Scholar

[3] 3. Lascarides, C. G. and Maddox, I. J., Matrix transformations between some classes of sequences, Proc. Camb. Phil. Soc, 68 (1970), 99-104. Google Scholar

[4] 4. Maddox, I. J., Spaces of strongly summable sequences, Quarterly J. of Math. Oxford, (2) 18 (1967), 345-355. Google Scholar

[5] 5. Maddox, I. J., On Kuttnefs theorem, J. London Math Soc, 43 (1968), 285-290. Google Scholar

[6] 6. Maddox, I. J., Paranormed sequence spaces generated by infinite matrices, Proc. Camb. Phil. Soc, 64 (1968), 335-340. Google Scholar

[7] 7. Maddox, I. J., Some properties of paranormed sequence spaces, J. London Math. Soc (2) 1 (1969), 316-322. Google Scholar

[8] 8. Maddox, I. J. and Roles, J. W., Absolute convexity in certain topological linear spaces, Proc Camb. Phil. Soc, 66 (1969), 541-545. Google Scholar

[9] 9. Simons, S., The sequence spaces l(p) and m(p), Proc. London Math. Soc (3) 15 (1965); 422-436. Google Scholar

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