Geodesic
A Short Proof of an Interpolation Theorem
Canadian mathematical bulletin, Tome 17 (1974) no. 1, pp. 127-128

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

In this note we give a simple proof of an operator-interpolation theorem (Theorem 2) due originally to Donoghue [6], and Lions-Foias [7].Let be the complex plane, the open upper half-plane, the real line, R+ and R- the non-negative and non-positive axes. Denote by the class of positive functions on which extend analytically to —R-, and map into itself. Denote by ’ the class of functions φ such that φ(x1/2)2 is in . 
Hughes, Edward. A Short Proof of an Interpolation Theorem. Canadian mathematical bulletin, Tome 17 (1974) no. 1, pp. 127-128. doi: 10.4153/CMB-1974-025-2
@article{10_4153_CMB_1974_025_2,
     author = {Hughes, Edward},
     title = {A {Short} {Proof} of an {Interpolation} {Theorem}},
     journal = {Canadian mathematical bulletin},
     pages = {127--128},
     year = {1974},
     volume = {17},
     number = {1},
     doi = {10.4153/CMB-1974-025-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-025-2/}
}
TY  - JOUR
AU  - Hughes, Edward
TI  - A Short Proof of an Interpolation Theorem
JO  - Canadian mathematical bulletin
PY  - 1974
SP  - 127
EP  - 128
VL  - 17
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-025-2/
DO  - 10.4153/CMB-1974-025-2
ID  - 10_4153_CMB_1974_025_2
ER  - 
%0 Journal Article
%A Hughes, Edward
%T A Short Proof of an Interpolation Theorem
%J Canadian mathematical bulletin
%D 1974
%P 127-128
%V 17
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-025-2/
%R 10.4153/CMB-1974-025-2
%F 10_4153_CMB_1974_025_2

[1] 1. Dunford, N. and Schwartz, J., Linear operators, Interscience, New York, 1963. Google Scholar

[2] 2. Heinz, E., Beiträge zur Störungstheorie der Spektralzerlegung, Math. Ann. 123 (1951), 415- 438. Google Scholar

[3] 3. Heinz, E., On an inequality of linear operators in a Hilbert space, Nat. Acad. Sci. (U.S.A.) 387 (1955), 27-29. Google Scholar

[4] 4. Löwner, K., Über monotone Matrix Functioned Math. Z. 38 (1934), 177-216. Google Scholar

[5] 5. Turner, R., On monotone operator functions and interpolation, (to appear). Google Scholar

[6] 6. Donoghue, W. F., The Interpolation Of Quadratic Norms, Acta Math. 118 (1967) 251-270. Google Scholar

[7] 7. Lions, J. L. and Foias, C., Sur certains théorémes d'interpolation, Acta Sci. Math. (Szeged) 22 (1961) 269-282. Google Scholar

Cité par Sources :