Geodesic
LINEAR FRACTIONAL RELATIONS IN BANACH SPACES: INTERIOR POINTS IN THE DOMAIN AND ANALOGUES OF THE LIOUVILLE THEOREM
Glasgow mathematical journal, Tome 49 (2007) no. 2, pp. 257-268

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

DOI

In this paper we study linear fractional relations defined in the following way. Let i, 'i, i = 1,2, be Banach spaces. We denote the space of bounded linear operators by . Let T ε ( 1 ⊕ 2, '1 ⊕ '2). To each such operator there corresponds a 2 × 2 operator matrix of the form(*) where T ij ε ( j , 'i . For each such T we define a set-valued map G T from ( 1, 2) into the set of closed affine subspaces of ('1, '2) by The map G T is called a linear fractional relation.The paper is devoted to the following two problems. • Characterization of operator matrices of the form (*) for which the set G T(K) is non-empty for each K in some open ball of the space (1,2). • Characterizations of quadruples (1, 2, '1, '2) of Banach spaces such that linear fractional relations defined for such spaces satisfy the natural analogue of the Liouville theorem “a bounded entire function is constant”.
DOI : 10.1017/S0017089507003539
Mots-clés : 47A56, 46B20, 47B50 
OSTROVSKII, M. I. LINEAR FRACTIONAL RELATIONS IN BANACH SPACES: INTERIOR POINTS IN THE DOMAIN AND ANALOGUES OF THE LIOUVILLE THEOREM. Glasgow mathematical journal, Tome 49 (2007) no. 2, pp. 257-268. doi: 10.1017/S0017089507003539
@article{10_1017_S0017089507003539,
     author = {OSTROVSKII, M. I.},
     title = {LINEAR {FRACTIONAL} {RELATIONS} {IN} {BANACH} {SPACES:} {INTERIOR} {POINTS} {IN} {THE} {DOMAIN} {AND} {ANALOGUES} {OF} {THE} {LIOUVILLE} {THEOREM}},
     journal = {Glasgow mathematical journal},
     pages = {257--268},
     year = {2007},
     volume = {49},
     number = {2},
     doi = {10.1017/S0017089507003539},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003539/}
}
TY  - JOUR
AU  - OSTROVSKII, M. I.
TI  - LINEAR FRACTIONAL RELATIONS IN BANACH SPACES: INTERIOR POINTS IN THE DOMAIN AND ANALOGUES OF THE LIOUVILLE THEOREM
JO  - Glasgow mathematical journal
PY  - 2007
SP  - 257
EP  - 268
VL  - 49
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003539/
DO  - 10.1017/S0017089507003539
ID  - 10_1017_S0017089507003539
ER  - 
%0 Journal Article
%A OSTROVSKII, M. I.
%T LINEAR FRACTIONAL RELATIONS IN BANACH SPACES: INTERIOR POINTS IN THE DOMAIN AND ANALOGUES OF THE LIOUVILLE THEOREM
%J Glasgow mathematical journal
%D 2007
%P 257-268
%V 49
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003539/
%R 10.1017/S0017089507003539
%F 10_1017_S0017089507003539

Cité par Sources :