46
Views
2
CrossRef citations to date
0
Altmetric
Research Article

Reflexivity of sets of isometries on bounded variation function spaces

Pages 4405-4415 | Received 16 Jun 2020, Accepted 10 Jan 2021, Published online: 01 Feb 2021

References

  • Kadison V. Local derivations. J Algebra. 1990;130:494–509.
  • Larson DR. Reflexivity, algebraic reflexivity and linear interpolation. Am J Math. 1988;110:283–299.
  • Larson DR, Sourour AR. Local derivations and local automorphisms of B(X). In Proc. Sympos. Pure Math., Part 2, vol. 51, Amer. Math. Soc., Providence, RI, pp. 187–194, 1990.
  • Molnár L. Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces. Springer; 2007.
  • Molnár L. The set of automorphisms of B(H) is topologically reflexive in B(B(H)). Studia Math. 1997;122:183–193.
  • Molnár L, Zalar B. Reflexivity of the group of surjective isometries on some Banach spaces. Proc Edinb Math Soc. 1999;42:17–36.
  • Botelho F, Jamison J. Algebraic and topological reflexivity of spaces of Lipschitz functions. Rev Roumaine Math Pures Appl. 2011;56(2):105–114.
  • Botelho F, Jamison J. Algebraic reflexivity of sets of bounded operators on vector valued Lipschitz functions. Linear Algebra Appl. 2010;432(12):3337–3342.
  • Cabello Sánchez F. Local isometries on spaces of continuous functions. Math Z. 2005;251(4):735–749.
  • Cabello Sánchez F, Molnár L. Reflexivity of the isometry group of some classical spaces. Rev Mat Iberoamericana. 2002;18(2):409–430.
  • Dutta S, Rao TSSRK. Algebraic reflexivity of some subsets of the isometry group. Linear Algebra Appl. 2008;429:1522–1527.
  • Hosseini M. Algebraic reflexivity of sets of bounded linear operators on absolutely continuous function spaces. Oper. Matrices. 2019;13(3):887–905.
  • Dutta S, Rao TSSRK. Local isometries of function spaces. Math Z. 2003;243:449–469.
  • Jiménez-Vargas A, Morales Campoy A, Villegas-Vallecillos M. Algebraic reflexivity of the isometry group of some spaces of Lipschitz functions. J Math Anal Appl. 2010;366(1):195–201.
  • Oi S. Algebraic reflexivity of isometry groups of algebras of Lipschitz maps. Linear Algebra Appl. 2019;566:167–182.
  • Fošner M, Ilišević D, Li CK. G-invariant norms and bicircular projections. Linear Algebra Appl. 2007;420:596–608.
  • Šemrl P. Local automorphisms and derivations on B(H). Proc Am Math Soc. 1997;125:2677–2680.
  • Molnár L. 2-local isometries on some operator algebras. Proc Edinburgh Math Soc. 2002;45:349–352.
  • Araujo J. Linear isometries between spaces of functions of bounded variation. Bull Austral Math Soc. 1999;59:335–341.
  • Jarosz K. Isometries in semisimple, commutative Banach algebras. Proc Am Math Soc. 1985;94(1):65–71.
  • Hatori O. Hermitian operators and isometries on Banach algebras of continuous maps with values in unital commutative C*-algebras. J Funct Spaces. 2018. Atricle ID 8085304, 14 pages.
  • Nagasawa M. Isomorphisms between commutative Banach algebras with an application to rings of analytic functions. Kodai Math Sem Rep. 1959;11:182–188.
  • Apostol TM. Mathematical Analysis, 2nd ed. Reading (MA): Addison-Wesley; 1974.
  • Hosseini M. 2-local isometries between spaces of functions of bounded variation. Positivity. 2019;24:1–9.
  • Li L, Peralta AM, Wang L, Wang Y-S. Weak-2-local isometries on uniform algebras and Lipschitz algebras. Publ. Mat. 2019;63(1):241–264.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.