Research Interests
Functional Analysis · Operator Theory · Spectral Theory
My research interests include functional analysis, operator theory, and spectral theory, with particular emphasis on norm and minimum attaining operators, absolutely norm attaining and absolutely minimum attaining operators, bounded and unbounded operators, perturbation theory, Moore–Penrose inverses, Aluthge transformations, quaternionic operator theory, invariant subspaces, operator algebras, and completely positive maps.
Journal Articles
2026
1. Sudip Ranjan Bhuia; G. Ramesh; Puspendu Nag; On the minimum modulus of dual truncated Toeplitz operators; Linear and Multilinear Algebra, 74 (2026), no. 11, 1563–1588.
2. Puspendu Nag; G. Ramesh; On absolutely norm (minimum) attaining block operator matrix; Journal of Mathematical Analysis and Applications, 563 (2026), no. 1, Paper No. 130742, 20 pp.
2025
3. G. Ramesh; M. Veena Sangeetha; Shanola S. Sequeira; Representation of compact operators between Banach spaces; Journal of Operator Theory, 94 (2025), no. 1, 3–21.
4. Bhumi Amin; G. Ramesh; Multiplicative and ternary domains of a completely positive map between Hilbert pro-C*-modules; Annals of Functional Analysis, 16 (2025), no. 3, Paper No. 57, 25 pp.
5. Neeru Bala; G. Ramesh; Hyperinvariant subspaces for normaloid essential isometric operators; Journal of Mathematical Analysis and Applications, 543 (2025), no. 2, part 2, Paper No. 128998, 10 pp.
2024
6. G. Ramesh; Shanola S. Sequeira; Representation and normality of hyponormal operators in the closure of AN-operators; Acta Mathematica Hungarica, 174 (2024), no. 2, 341–359.
7. Bhumi Amin; G. Ramesh; Completely positive maps: pro-C*-algebras and Hilbert modules over pro-C*-algebras; Positivity, 28 (2024), no. 5, Paper No. 71, 19 pp.
2023
8. Bhumi Amin; G. Ramesh; Linear and multiplicative maps under spectral conditions; Functional Analysis and Its Applications, 57 (2023), no. 3, 179–191.
9. Ramesh, G.; Sequeira, Shanola S.; On the closure of absolutely norm attaining operators; Linear and Multilinear Algebra, 71 (2023), no. 18, 2894–2914.
10. S. H. Kulkarni; G. Ramesh; Spectral representation of absolutely minimum attaining unbounded normal operators; Operators and Matrices, 17 (2023), no. 3, 653–669.
11. G. Ramesh; B. Sudip Ranjan; D. Venku Naidu; On the C-polar decomposition of operators and applications; Monatshefte für Mathematik, 202 (2023), no. 3, 583–598.
12. G. Ramesh; Shanola S. Sequeira; Absolutely minimum attaining Toeplitz and absolutely norm attaining Hankel operators; Comptes Rendus Mathématique, 361 (2023), 973–977.
13. G. Ramesh; Hiroyuki Osaka; Yoichi Udagawa; Takeaki Yamazaki; Stability of the AN-property for the induced Aluthge transformations; Linear Algebra and its Applications, 678 (2023), 206–226.
14. G. Ramesh; H. Osaka; Y. Udagawa; T. Yamazaki; Stability of AN-operators under functional calculus; Analysis Mathematica, 49 (2023), no. 3, 825–839.
15. G. Ramesh; B. Sudip Ranjan; D. Venku Naidu; A representation of compact C-normal operators; Linear and Multilinear Algebra, 71 (2023), no. 9, 1565–1577.
2022
16. G. Ramesh; B. Sudip Ranjan; D. Venku Naidu; Cartesian decomposition of C-normal operators; Linear and Multilinear Algebra, 70 (2022), no. 21, 6640–6647.
17. G. Ramesh; B. Sudip Ranjan; D. Venku Naidu; Cyclic composition operators on Segal-Bargmann space; Concrete Operators, 9 (2022), no. 1, 127–138.
18. Ramesh, G.; Sequeira, Shanola S.; Absolutely norm attaining Toeplitz and absolutely minimum attaining Hankel operators; Journal of Mathematical Analysis and Applications, 516 (2022), no. 1, Paper No. 126497, 12 pp.
19. G. Ramesh; H. Osaka; On operators which attain their norm on every reducing subspace; Annals of Functional Analysis, 13 (2022), no. 2, Paper No. 19, 13 pp.
2021
20. Neeru Bala; G. Ramesh; Weyl's theorem for commuting tuples of paranormal and *-paranormal operators; Bulletin of the Polish Academy of Sciences — Mathematics, 69 (2021), no. 1, 69–86.
21. Neeru Bala; G. Ramesh; A representation of hyponormal absolutely norm attaining operators; Bulletin des Sciences Mathématiques, 171 (2021), Paper No. 103020, 15 pp.
22. S. H. Kulkarni; G. Ramesh; Absolutely minimum attaining closed operators; Journal of Analysis, 29 (2021), no. 2, 473–492.
23. G. Ramesh; T. S. S. R. K. Rao; K. C. Sivakumar; International Conference cum Workshop on Analysis and its Applications June 18–22, 2018 Indian Institute of Technology Madras, Chennai, India; Journal of Analysis, 29 (2021), no. 2, 359–367.
24. Neeru Bala; G. Ramesh; A Bishop-Phelps-Bollobás type property for minimum attaining operators; Operators and Matrices, 15 (2021), no. 2, 497–513.
25. G. Ramesh; Osaka, Hiroyuki; On a subclass of norm attaining operators; Acta Scientiarum Mathematicarum (Szeged), 87 (2021), no. 1–2, 247–263.
2020
26. S. H. Kulkarni; G. Ramesh; Operators that attain reduced minimum; Indian Journal of Pure and Applied Mathematics, 51 (2020), no. 4, 1615–1631.
27. G. Ramesh; Hiroyuki Osaka; Linear maps preserving AN-operators; Bulletin of the Korean Mathematical Society, 57 (2020), no. 4, 831–838.
28. Neeru Bala; G. Ramesh; Weyl's theorem for paranormal closed operators; Annals of Functional Analysis, 11 (2020), no. 3, 567–582.
29. Neeru Bala; G. Ramesh; Spectral properties of absolutely minimum attaining operators; Banach Journal of Mathematical Analysis, 14 (2020), no. 3, 630–649.
30. G. Ramesh; P. Santhosh Kumar; Spectral theorem for quaternionic normal operators: multiplication form; Bulletin des Sciences Mathématiques, 159 (2020), 102840, 25 pp.
2019
31. D. Venku Naidu; G. Ramesh; On absolutely norm attaining operators; Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 129 (2019), no. 4, Paper No. 54, 17 pp.
2018
32. S. H. Kulkarni; G. Ramesh; On the denseness of minimum attaining operators; Operators and Matrices, 12 (2018), no. 3, 699–709.
33. Ganesh, J.; Ramesh, G.; Sukumar, D.; A characterization of absolutely minimum attaining operators; Journal of Mathematical Analysis and Applications, 468 (2018), no. 1, 567–583.
34. Ramesh, G.; Absolutely norm attaining paranormal operators; Journal of Mathematical Analysis and Applications, 465 (2018), no. 1, 547–556.
35. Ganesh, Jadav; G. Ramesh; Sukumar, Daniel; Perturbation of minimum attaining operators; Advances in Operator Theory, 3 (2018), no. 3, 473–490.
2017
36. G. Ramesh; P. Santhosh Kumar; Spectral theorem for quaternionic compact normal operators; Journal of Analysis, 25 (2017), no. 1, 65–81.
37. G. Ramesh; On the numerical radius of a quaternionic normal operator; Advances in Operator Theory, 2 (2017), no. 1, 78–86.
38. G. Ramesh; P. Santhosh Kumar; Borel functional calculus for quaternionic normal operators; Journal of Mathematical Physics, 58 (2017), no. 5, 053501, 16 pp.
2016
39. Kurmayya, T.; Ramesh, G.; Cone nonnegativity of Moore-Penrose inverses of unbounded Gram operators; Annals of Functional Analysis, 7 (2016), no. 2, 338–347.
40. Ramesh, G.; Weyl-von Neumann-Berg theorem for quaternionic operators; Journal of Mathematical Physics, 57 (2016), no. 4, 043503, 7 pp.
41. G. Ramesh; P. Santhosh Kumar; On the polar decomposition of right linear operators in quaternionic Hilbert spaces; Journal of Mathematical Physics, 57 (2016), no. 4, 043502, 16 pp.
2015
42. Ganesh, Jadav; G. Ramesh; Sukumar, Daniel; On the structure of absolutely minimum attaining operators; Journal of Mathematical Analysis and Applications, 428 (2015), no. 1, 457–470.
2014
43. Ramesh, G.; Structure theorem for AN-operators; Journal of the Australian Mathematical Society, 96 (2014), no. 3, 386–395.
2013
44. Ramesh, G.; McIntosh formula for the gap between regular operators; Banach Journal of Mathematical Analysis, 7 (2013), no. 1, 97–106.
2012
45. B. V. Rajarama Bhat; G. Ramesh; K. Sumesh; Stinespring's theorem for maps on Hilbert C*-modules; Journal of Operator Theory, 68 (2012), no. 1, 173–178.
2011
46. S. H. Kulkarni; G. Ramesh; Approximation of Moore-Penrose inverse of a closed operator by a sequence of finite rank outer inverses; Functional Analysis, Approximation and Computation, 3 (2011), no. 1, 23–32.
47. Ramesh, G.; The Horn-Li-Merino formula for the gap and the spherical gap of unbounded operators; Proceedings of the American Mathematical Society, 139 (2011), no. 3, 1081–1090.
48. S. H. Kulkarni; G. Ramesh; The carrier graph topology; Banach Journal of Mathematical Analysis, 5 (2011), no. 1, 56–69.
2010
49. S. H. Kulkarni; G. Ramesh; Projection methods for computing Moore-Penrose inverses of unbounded operators; Indian Journal of Pure and Applied Mathematics, 41 (2010), no. 5, 647–662.
50. S. H. Kulkarni; G. Ramesh; A formula for gap between two closed operators; Linear Algebra and its Applications, 432 (2010), no. 11, 3012–3017.
2008
51. S. H. Kulkarni; M. T. Nair; G. Ramesh; Some properties of unbounded operators with closed range; Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 118 (2008), no. 4, 613–625.
52. S. H. Kulkarni; G. Ramesh; Projection methods for inversion of unbounded operators; Indian Journal of Pure and Applied Mathematics, 39 (2008), no. 2, 185–202.
Book Chapters
1. S. H. Kulkarni; G. Ramesh; Singular value decomposition of unbounded absolutely minimum attaining operators; in Recent Developments in Spectral and Approximation Theory, Trends in Mathematics, Birkhäuser/Springer, Cham, 2025, 19–35.
2. S. H. Kulkarni; G. Ramesh; Absolutely minimum attaining closed operators: a survey; in Inverse problems, regularization methods and related topics—a volume in honour of Thamban Nair, 273–302, Springer, Singapore, 2025.
Corrections and Errata
Bhumi Amin; G. Ramesh; Correction: Completely positive maps: pro-C*-algebras and Hilbert modules over pro-C*-algebras; Positivity, 30 (2026), no. 1, Paper No. 15, 3 pp.
To Appear
The following article has been accepted for publication and is listed separately from communicated and unpublished work.
G. Ramesh, Hiroyuki Osaka and Shanola Sequeira; Denseness of a subclass of norm attaining operators with invariant subspaces. [To appear in Journal of Operator Theory.]
Communicated Articles
These articles have been communicated/submitted for publication and are separate from the published-work count.
Puspendu Nag and G. Ramesh; Minimum Attaining Operators on Reducing Subspaces: Spectral Structure and Density. [Communicated.]
Neeru Bala and G. Ramesh; Spectral Characterizations of Schatten-Class Perturbations of Partial Isometries. [Communicated.]
Neeru Bala and G. Ramesh; Trace class perturbation of bounded operators. [Communicated.]
Bhumi Amin and G. Ramesh; A Radon-Nikodym theorem for completely positive maps on Hilbert pro-C*-modules. [Communicated.]
Weyl-von Neumann theorem for antilinear skew-self-adjoint operators. [Communicated.]
Other Unpublished Work
S. H. Kulkarni and G. Ramesh; Perturbation of closed range operators and Moore-Penrose inverse.
B. Sudip Ranjan, D. Venku Naidu and G. Ramesh; Boundedness and compactness of linear combinations of composition operators between Segal-Bargmann spaces.
Neeru Bala and G. Ramesh; Almost invariant half-space for closed operators.