The conjugate of a product of linear relations

Jaftha, Jacob J.. "The conjugate of a product of linear relations." Commentationes Mathematicae Universitatis Carolinae 47.2 (2006): 265-273. <http://eudml.org/doc/249842>.

@article{Jaftha2006,
abstract = {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 $(ST)^\{\prime \}=T^\{\prime \}S^\{\prime \}$. 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.},
author = {Jaftha, Jacob J.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {linear relations; conjugates; linear operators; linear relation; conjugate; linear operator},
language = {eng},
number = {2},
pages = {265-273},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The conjugate of a product of linear relations},
url = {http://eudml.org/doc/249842},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Jaftha, Jacob J.
TI - The conjugate of a product of linear relations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 2
SP - 265
EP - 273
AB - 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 $(ST)^{\prime }=T^{\prime }S^{\prime }$. 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.
LA - eng
KW - linear relations; conjugates; linear operators; linear relation; conjugate; linear operator
UR - http://eudml.org/doc/249842
ER -