Geodesic
Convex operator functions
Sbornik. Mathematics, Tome 17 (1972) no. 2, pp. 269-277

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\varphi(x)$ be a convex downwards function, $A>0$ a selfadjoint operator in a Hilbert space $H$, $P$ an orthogonal projector in $H$; suppose $D_A\cap PH$ is dense in $PH$, and let $A_p$ be the Friedrichs extension of the operator $PAP$ defined on $D_A\cap PH$. The inequality $\mathrm{Sp}\varphi(A_p)\leqslant\mathrm{Sp}\varphi(PAP)$ is proved. An estimate for the Jacobi $\theta$-function and a distant generalization of the Szasz inequality are obtained as corollaries. Bibliography: 3 titles. 
@article{SM_1972_17_2_a7,
     author = {F. A. Berezin},
     title = {Convex operator functions},
     journal = {Sbornik. Mathematics},
     pages = {269--277},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1972_17_2_a7/}
}
TY  - JOUR
AU  - F. A. Berezin
TI  - Convex operator functions
JO  - Sbornik. Mathematics
PY  - 1972
SP  - 269
EP  - 277
VL  - 17
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1972_17_2_a7/
LA  - en
ID  - SM_1972_17_2_a7
ER  - 
%0 Journal Article
%A F. A. Berezin
%T Convex operator functions
%J Sbornik. Mathematics
%D 1972
%P 269-277
%V 17
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1972_17_2_a7/
%G en
%F SM_1972_17_2_a7
F. A. Berezin. Convex operator functions. Sbornik. Mathematics, Tome 17 (1972) no. 2, pp. 269-277. http://geodesic.mathdoc.fr/item/SM_1972_17_2_a7/