Geodesic
The conjugate of a product of linear relations
Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 2, pp. 265-273.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Let $X$, $Y$ and $Z$ be normed linear spaces with $T(X\rightarrow Y)$ and $S(Y\rightarrow Z)$ linear relations, i.e. setvalued maps. We seek necessary and sufficient conditions that would ensure that $(ST)'=T'S'$. First, we cast the concepts of relative boundedness and co-continuity in the set valued case and establish a duality. This duality turns out to be similar to the one that exists for densely defined linear operators and is then used to establish the necessary and sufficient conditions. These conditions are similar to those for the single valued case. In the process, the well known characterisation of relativeboundedness for closed linear operators by Sz.-Nagy is extended to the multivalued linear maps and we compare our results to other known necessary and sufficient conditions.
Classification : 47A05, 47A06
Keywords: linear relations; conjugates; linear operators 
@article{CMUC_2006__47_2_a5,
     author = {Jaftha, J. J.},
     title = {The conjugate of a product of linear relations},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {265--273},
     publisher = {mathdoc},
     volume = {47},
     number = {2},
     year = {2006},
     mrnumber = {2241531},
     zbl = {1150.47002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2006__47_2_a5/}
}
TY  - JOUR
AU  - Jaftha, J. J.
TI  - The conjugate of a product of linear relations
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2006
SP  - 265
EP  - 273
VL  - 47
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2006__47_2_a5/
LA  - en
ID  - CMUC_2006__47_2_a5
ER  - 
%0 Journal Article
%A Jaftha, J. J.
%T The conjugate of a product of linear relations
%J Commentationes Mathematicae Universitatis Carolinae
%D 2006
%P 265-273
%V 47
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2006__47_2_a5/
%G en
%F CMUC_2006__47_2_a5
Jaftha, J. J. The conjugate of a product of linear relations. Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 2, pp. 265-273. http://geodesic.mathdoc.fr/item/CMUC_2006__47_2_a5/