Geodesic
An Extrapolation Theorem for Positive Operators
Canadian journal of mathematics, Tome 30 (1978) no. 2, pp. 225-230

Voir la notice de l'article provenant de la source Cambridge University Press

Denote by S and M respectively the complex vector spaces of simple and measurable complex valued functions defined on the finite measure space X. Let T be a positive linear map from S to M such that for each p, 1 < p < ∞, sup {||T f||p: f ∈ S, ||f||P ≦ 1} is finit. finite. T then has an extension to a bounded transformation of every LP(X), 1 < p < ∞ , and these extensions are "consistent". The norm of T as a transformation of Lp is denoted ||T||P. The aim of this note is to prove the following theorem. 
Miller, H. D. B. An Extrapolation Theorem for Positive Operators. Canadian journal of mathematics, Tome 30 (1978) no. 2, pp. 225-230. doi: 10.4153/CJM-1978-020-6
@article{10_4153_CJM_1978_020_6,
     author = {Miller, H. D. B.},
     title = {An {Extrapolation} {Theorem} for {Positive} {Operators}},
     journal = {Canadian journal of mathematics},
     pages = {225--230},
     year = {1978},
     volume = {30},
     number = {2},
     doi = {10.4153/CJM-1978-020-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1978-020-6/}
}
TY  - JOUR
AU  - Miller, H. D. B.
TI  - An Extrapolation Theorem for Positive Operators
JO  - Canadian journal of mathematics
PY  - 1978
SP  - 225
EP  - 230
VL  - 30
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1978-020-6/
DO  - 10.4153/CJM-1978-020-6
ID  - 10_4153_CJM_1978_020_6
ER  - 
%0 Journal Article
%A Miller, H. D. B.
%T An Extrapolation Theorem for Positive Operators
%J Canadian journal of mathematics
%D 1978
%P 225-230
%V 30
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1978-020-6/
%R 10.4153/CJM-1978-020-6
%F 10_4153_CJM_1978_020_6

[1] 1. Garsia, A., Topics in almost everywhere convergence (Markham, Chicago). Google Scholar

[2] 2. Rudin, W., Real and complex analysis (McGraw-Hill, 1974). Google Scholar

[3] 3. Stein, E. M., Topics in harmonic analysis (Princeton, 1970). Google Scholar

[4] 4. Yosida, K., Functional analysis, 4th Ed. (Springer, 1974). Google Scholar

Cité par Sources :