Maps on idempotent operators

• Autorzy: Peter Šemrl
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47B49: Transformers, preservers (operators on spaces of operators)
• 46C05: Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2007
• Tom: 75
• Numer: 1
• Strony: 289-301

Daty

wydano

2007

Twórcy

autor

Peter Šemrl

• Department of Mathematics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia

Identyfikatory

DOI

10.4064/bc75-0-17