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Research Article

On the closure of absolutely norm attaining operators

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Pages 2894-2914 | Received 07 Feb 2022, Accepted 15 Aug 2022, Published online: 29 Sep 2022

References

  • Bishop E, Phelps RR. A proof that every Banach space is subreflexive. Bull Amer Math Soc. 1961;67:97–98.
  • Lindenstrauss J. On operators which attain their norm. Israel J Math. 1963;1:139–148.
  • Acosta MD. Denseness of norm attaining mappings. RACSAM Rev R Acad Cienc Exactas Fís Nat Ser A Mat. 2006;100(1–2):9–30.
  • Enflo P, Kover J, Smithies L. Denseness for norm attaining operator-valued functions. Linear Algebra Appl. 2001;338:139–144.
  • Carvajal X, Neves W. Operators that achieve the norm. Integral Equ Oper Theory. 2012;72(2):179–195.
  • Pandey SK, Paulsen VI. A spectral characterization of AN operators. J Aust Math Soc. 2017;102(3):369–391.
  • Ramesh G. Structure theorem for AN-operators. J Aust Math Soc. 2014;96(3):386–395.
  • Ramesh G. Absolutely norm attaining paranormal operators. J Math Anal Appl. 2018;465(1):547–556.
  • Venku Naidu D, Ramesh G. On absolutely norm attaining operators. Proc Indian Acad Sci Math Sci. 2019;129(4). Article ID 54, 17 pp.
  • Ganesh J, Ramesh G, Sukumar D. A characterization of absolutely minimum attaining operators. J Math Anal Appl. 2018;468(1):567–583.
  • Kulkarni SH, Ramesh G. On the denseness of minimum attaining operators. Oper Matrices. 2018;12(3):699–709.
  • Bala N, Golla R. Spectral properties of absolutely minimum attaining operators. Banach J Math Anal. 2020;14(3):630–649.
  • Bala N, Ramesh G. Hyperinvariant subspace for absolutely norm attaining and absolutely minimum attaining operators. Preprint (https://arxiv.org/abs/2002.09167).
  • Conway JB. A course in functional analysis. 2nd ed. Graduate Texts in Mathematics, 96. New York: Springer-Verlag; 1990.
  • Gohberg I, Goldberg S, Kaashoek MA. Basic classes of linear operators. Basel: Birkhäuser Verlag; 2003.
  • Halmos PR. A Hilbert space problem book. 2nd ed. Encyclopedia of Mathematics and its Applications, 17. Graduate Texts in Mathematics, 19. New York: Springer-Verlag; 1982.
  • Kubrusly CS. The elements of operator theory. 2nd ed. New York: Birkhäuser/Springer; 2011.
  • Golla R, Osaka H. Linear maps preserving AN-operators. Bull Korean Math Soc. 2020;57(4):831–838.
  • Carvajal X, Neves W. Operators that attain their minima. Bull Braz Math Soc (N.S.). 2014;45(2):293–312.
  • Schmüdgen K. Unbounded self-adjoint operators on Hilbert space. Graduate Texts in Mathematics, 265. Dordrecht: Springer; 2012.
  • Reed M, Simon B. Methods of modern mathematical physics. I. 2nd ed. New York: Academic Press, Inc.; 1980.
  • Müller V. Spectral theory of linear operators and spectral systems in Banach algebras. 2nd ed. Operator Theory: Advances and Applications, 139. Basel: Birkhäuser Verlag; 2007.
  • Simon B. Operator theory. A Comprehensive Course in Analysis, Part 4. Providence (RI): American Mathematical Society; 2015.
  • Bouldin R. The essential minimum modulus. Indiana Univ Math J. 1981;30(4):513–517.
  • Pedersen GK. Analysis now. Graduate Texts in Mathematics, 118. New York: Springer-Verlag; 1989.
  • Kaufman WE. A stronger metric for closed operators in Hilbert space. Proc Amer Math Soc. 1984;90(1):83–87.
  • Halmos PR, Wallen LJ. Powers of partial isometries. J Math Mech. 1969/1970;19:657–663.

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