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
@article{10_4153_CMB_1975_013_7,
author = {Maddox, I. J. and Roles, J. W.},
title = {Absolute {Convexity} in {Spaces} of {Strongly} {Summable} {Sequences}},
journal = {Canadian mathematical bulletin},
pages = {67--75},
year = {1975},
volume = {18},
number = {1},
doi = {10.4153/CMB-1975-013-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-013-7/}
}
TY - JOUR AU - Maddox, I. J. AU - Roles, J. W. TI - Absolute Convexity in Spaces of Strongly Summable Sequences JO - Canadian mathematical bulletin PY - 1975 SP - 67 EP - 75 VL - 18 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-013-7/ DO - 10.4153/CMB-1975-013-7 ID - 10_4153_CMB_1975_013_7 ER -
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