JEDNOSTKA NAUKOWA KATEGORII A+

Artykuły w formacie PDF dostępne są dla subskrybentów, którzy zapłacili za dostęp online, po podpisaniu licencji Licencja użytkownika instytucjonalnego. Czasopisma do 2009 są ogólnodostępne (bezpłatnie).

Rigidity of isometries on idempotents

Tom 279 / 2024

Wenhua Qian, Yudi Shi, Wenming Wu, Zhang Xiang, Wei Yuan Studia Mathematica 279 (2024), 273-291 MSC: Primary 47B49; Secondary 54E40 DOI: 10.4064/sm240124-2-8 Opublikowany online: 20 November 2024

Streszczenie

Wigner’s unitary-antiunitary theorem, which states that every surjective isometry on the Grassmann space of rank one projections is induced by a unitary or an antiunitary, characterizes the rigidity of isometries on projections. We introduce the concept of quasi-lines and characterize their forms. By using the geometrical characterizations of quasi-lines, we can distinguish projections from non-self-adjoint idempotents. Then it is shown that every surjective isometry on the set of rank one idempotents is a unitary or an antiunitary similarity transformation possibly composed with the adjoint operation. This leads to a rigidity result for isometries on all idempotents, which states that every surjective isometry on the set of all nontrivial idempotents acting on a separable Hilbert space is a unitary or an antiunitary similarity transformation possibly composed with the adjoint operation or the complement operation.

Autorzy

  • Wenhua QianSchool of Mathematical Sciences
    Chongqing Normal University
    Chongqing 401331, China
    e-mail
  • Yudi ShiInstitute of Mathematics
    Academy of Mathematics and Systems Science
    Chinese Academy of Sciences
    Beijing 100190, China
    e-mail
  • Wenming WuSchool of Mathematical Sciences
    Chongqing Normal University
    Chongqing 401331, China
    e-mail
  • Zhang XiangSchool of Mathematics and Statistics
    Beijing Institute of Technology
    Beijing 100081, China
    e-mail
  • Wei YuanInstitute of Mathematics
    Academy of Mathematics and Systems Science
    Chinese Academy of Sciences
    Beijing 100190, China
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek