On Continuous Linear Transformations of Integral Type
Canadian mathematical bulletin, Tome 2 (1959) no. 3, pp. 163-166
Voir la notice de l'article provenant de la source Cambridge
Let (XxY, SxT, μxν) denote the completion of the Cartesian product of the σ-finite and complete "measure spaces (X, S, μ.) and (Y, T, ν) [3]. Let λx and λy denote arbitrary length functions defined on (X, S, μ.) and (Y, T, ν) respectively, the conjugate length functions [2]. We suppose that 1 is defined for every f(x, y) measurable (SxT). The Fubini theorem implies that f(x, y) is measurable (T) for almost all x. Thus λ xy(f) will be defined when λy(f) Is measurable (S). If Lλ y = Lp, 1 ≤ p < ∞, this is implied by the Fubini theorem. General conditions ensuring that λ y (f) is measurable (S) are given in [l, Theorem 3.2] When λxy(f) is defined for every f(x, y) measurable (SxT), it is a length function and Lλ xy is a Banach space [l, Theorem 3.l].
Ellis, H.W.; Mott, T.E. On Continuous Linear Transformations of Integral Type. Canadian mathematical bulletin, Tome 2 (1959) no. 3, pp. 163-166. doi: 10.4153/CMB-1959-021-1
@article{10_4153_CMB_1959_021_1,
author = {Ellis, H.W. and Mott, T.E.},
title = {On {Continuous} {Linear} {Transformations} of {Integral} {Type}},
journal = {Canadian mathematical bulletin},
pages = {163--166},
year = {1959},
volume = {2},
number = {3},
doi = {10.4153/CMB-1959-021-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1959-021-1/}
}
TY - JOUR AU - Ellis, H.W. AU - Mott, T.E. TI - On Continuous Linear Transformations of Integral Type JO - Canadian mathematical bulletin PY - 1959 SP - 163 EP - 166 VL - 2 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1959-021-1/ DO - 10.4153/CMB-1959-021-1 ID - 10_4153_CMB_1959_021_1 ER -
Cité par Sources :