EXTREME POINT METHODS IN THE STUDY OF ISOMETRIES ON CERTAIN NONCOMMUTATIVE SPACES
Glasgow mathematical journal, Tome 64 (2022) no. 2, pp. 462-483
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In this paper, we characterize surjective isometries on certain classes of noncommutative spaces associated with semi-finite von Neumann algebras: the Lorentz spaces $L^{w,1}$, as well as the spaces $L^1+L^\infty$ and $L^1\cap L^\infty$. The technique used in all three cases relies on characterizations of the extreme points of the unit balls of these spaces. Of particular interest is that the representations of isometries obtained in this paper are global representations.
JAGER, PIERRE DE; CONRADIE, JURIE. EXTREME POINT METHODS IN THE STUDY OF ISOMETRIES ON CERTAIN NONCOMMUTATIVE SPACES. Glasgow mathematical journal, Tome 64 (2022) no. 2, pp. 462-483. doi: 10.1017/S0017089521000227
@article{10_1017_S0017089521000227,
author = {JAGER, PIERRE DE and CONRADIE, JURIE},
title = {EXTREME {POINT} {METHODS} {IN} {THE} {STUDY} {OF} {ISOMETRIES} {ON} {CERTAIN} {NONCOMMUTATIVE} {SPACES}},
journal = {Glasgow mathematical journal},
pages = {462--483},
year = {2022},
volume = {64},
number = {2},
doi = {10.1017/S0017089521000227},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089521000227/}
}
TY - JOUR AU - JAGER, PIERRE DE AU - CONRADIE, JURIE TI - EXTREME POINT METHODS IN THE STUDY OF ISOMETRIES ON CERTAIN NONCOMMUTATIVE SPACES JO - Glasgow mathematical journal PY - 2022 SP - 462 EP - 483 VL - 64 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089521000227/ DO - 10.1017/S0017089521000227 ID - 10_1017_S0017089521000227 ER -
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