D-hyponormal and D-quasi-hyponormal Operators
DOI:
https://doi.org/10.26713/cma.v13i3.1708Keywords:
Drazin inverse, D-hyponormal operator, D-quasi-hyponormal operator, Fuglede-Putnam theoremAbstract
New classes of operators named D-hyponormal, and D-quasi-hyponormal are introduced in this paper. Some basic properties of these operators are presented. An investigation of extensions of the Fuglede-Putnam theorem for D-hyponormal operators is given.
Downloads
References
A. Bachir and M. W. Altanji, An asymmetric Putnam-Fuglede theorem for (p,k)-quasiposinormal operators, International Journal of Contemporary Mathematical Sciences 11(4) (2016), 165 – 172, DOI: 10.12988/IJCMS.2016.51051.
A. N. Bakir and S. Mecheri, Another version of Fuglede-Putnam theorem, Georgian Mathematical Journal 16(3) (2009), 427 – 433, DOI: 10.1515/GMJ.2009.427.
A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, Vol. 15, Springer, New York (2003), DOI: 10.1007/b97366.
S. K. Berberian, Extension of a theorem of Fuglede and Putnam, Proceedings of the American Mathematical Society 71(1) (1978), 113 – 114, DOI: 10.1090/S0002-9939-1978-0487554-2.
E. A. Bishop, A duality theorem for an arbitrary operator, Pacific Journal of Mathematics 9(2) (1959), 379 – 397, DOI: 10.2140/pjm.1959.9.379.
S. L. Campbell and C. D. Meyer, Generalized Inverse of Linear Transformations, Classics in Applied Mathematics series, xxiv + 264, SIAM (2009), DOI: 10.1137/1.9780898719048.
S. R. Caradus, Operator Theory of the Generalized Inverse, Science Press, New York (2004).
J. B. Conway, A Course in Functional Analysis, 2nd edition, Graduate Texts in Mathematics series (GTM, Vol. 96) Springer-Verlag, New York (1985), DOI: 10.1007/978-1-4757-3828-5.
M. Dana and R. Yousefi, On the classes of D-normal operators and D-quasi-normal operators on Hilbert space, Operators and Matrices 12(2) (2018), 465 – 487, DOI: 10.7153/oam-2018-12-29.
M. Dana and R. Yousefi, Generalizations of some classical theorems to D-normal operators on Hilbert spaces, Journal of Inequalities and Applications 2020 (2020), Article number: 101, DOI: 10.1186/s13660-020-02367-z.
B. Fuglede, A commutativity theorem for normal operators, Proceedings of the National Academy of Sciences 36(1) (1950), 35 – 40, DOI: 10.1073/pnas.36.1.35.
T. Furuta, On relaxation of normality in the Fuglede-Putnam theorem, Proceedings of the American Mathematical Society 77(3) (1979), 324 – 328, DOI: 10.1090/S0002-9939-1979-0545590-2.
P. R. Halmos, A Hilbert Space Problem Book, Graduate Texts in Mathematics series (GTM, Vol. 19), Springer-Verlag, New York (1982), DOI: 10.1007/978-1-4684-9330-6.
K. Laursen and M. Neumann, An Introduction to Local Spectral Theory, London Mathematical Society Monographs New Series, Vol. 20, Clarendon Press, Oxford (2000).
J. S. I. Mary and P. Vijayalakshmi, Fuglede-Putnam theorem and quasi-nilpotent part of n-power operators, Tamkang Journal of Mathematics 46(2) (2015), 151 – 165, DOI: 10.5556/j.tkjm.46.2015.1665.
S. Mecheri, Finite operators, Demonstratio Mathematica 35(2) (2002), 357 – 366, DOI: 10.1515/dema-2002-0216.
H. Messaoudene, Finite operators, Journal of Mathematics and System Science 3(4) (2013), 190 – 194.
M. H. Mortad, Yet more versions of the Fuglede-Putnam theorem, Glasgow Mathematical Journal 51(3) (2009), 473 – 480, DOI: 10.1017/S0017089509005114.
C. R. Putnam, On normal operators in Hilbert space, American Journal of Mathematics 73(2) (1951), 357 – 362, DOI: 10.2307/2372180.
J. P. Williams, Finite operators, Proceedings of the American Mathematical Society 26(1) (1970), 129 – 135, DOI: 10.1090/S0002-9939-1970-0264445-6.




