Maps on idempotent operators

Peter Šemrl. "Maps on idempotent operators." Banach Center Publications 75.1 (2007): 289-301. <http://eudml.org/doc/282118>.

@article{PeterŠemrl2007,
abstract = {The set of all bounded linear idempotent operators on a Banach space X is a poset with the partial order defined by P ≤ Q if PQ = QP = P. Another natural relation on the set of idempotent operators is the orthogonality relation defined by P ⊥ Q ⇔ PQ = QP = 0. We briefly survey known theorems on maps on idempotents preserving order or orthogonality. We discuss some related results and open problems. The connections with physics, geometry, theory of automorphisms, and linear preserver problems will be explained. At the end we will prove a new result concerning bijective maps on idempotent operators preserving comparability.},
author = {Peter Šemrl},
journal = {Banach Center Publications},
language = {eng},
number = {1},
pages = {289-301},
title = {Maps on idempotent operators},
url = {http://eudml.org/doc/282118},
volume = {75},
year = {2007},
}

TY - JOUR
AU - Peter Šemrl
TI - Maps on idempotent operators
JO - Banach Center Publications
PY - 2007
VL - 75
IS - 1
SP - 289
EP - 301
AB - The set of all bounded linear idempotent operators on a Banach space X is a poset with the partial order defined by P ≤ Q if PQ = QP = P. Another natural relation on the set of idempotent operators is the orthogonality relation defined by P ⊥ Q ⇔ PQ = QP = 0. We briefly survey known theorems on maps on idempotents preserving order or orthogonality. We discuss some related results and open problems. The connections with physics, geometry, theory of automorphisms, and linear preserver problems will be explained. At the end we will prove a new result concerning bijective maps on idempotent operators preserving comparability.
LA - eng
UR - http://eudml.org/doc/282118
ER -