پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 679 |
| تعداد مقالات | 9,900 |
| تعداد مشاهده مقاله | 70,092,018 |
| تعداد دریافت فایل اصل مقاله | 49,408,259 |
Fuglede-Putnam type theorems for extension of $\ast$-class $A$ operators | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 72، دوره 13، شماره 2، مهر 2022، صفحه 863-873 اصل مقاله (387.96 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.21260.2243 | ||
| نویسنده | ||
| Mohammad Rashid* | ||
| Department of Mathematics & Statistics, Faculty of Science, P.O.Box 7, Mu'tah University, Al-Karak, Jordan | ||
| تاریخ دریافت: 12 شهریور 1399، تاریخ بازنگری: 27 آبان 1399، تاریخ پذیرش: 23 فروردین 1400 | ||
| چکیده | ||
| In this article, we consider $k$-quasi-$\ast$-class $A$ operator $T\in\bh$ such that $TX=XS$ for some $X\in \bkh$ and prove the Fuglede-Putnam type theorem when adjoint of $S\in\bk$ is $k$-quasi-$\ast$-class $A$ or dominant operators. Among other things, we prove that two quasisimilar $k$-quasi-$\ast$-class $A$ operators have equal essential spectra. | ||
| کلیدواژهها | ||
| $ast$-class $A$ operators؛ $k$-quasi-$ast$-class $A$ operators؛ quasisimilar operators | ||
| مراجع | ||
|
[1] P. Aiena, Fredholm and local spectral theory with applications to multipliers, Kluwer, 2004. [2] S.C. Arora and J.K. Thukral, On a class of operators, Glas. Math. Ser. III 21 (1986), 381–386. [3] A. Bachir and P. Pagacz, An asymmetric Putnam-Fuglede theorem for ∗-paranormal operators, arXiv:1405.4844 (2018). [4] E. Bishop, A duality theorem for an arbitrary operator, Pacific J. Math. 9 (1959), no. 2, 379–397. [5] I.H. Jeon B.P. Duggal and I.H. Kim, On ∗-paranormal contractions and properties for ∗-class A operators, Linear Algebra Appl. 436 (2012), 954–962. [6] R.G. Douglas, On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc. 17 (1966), 413–415. [7] T. Furuta, Invitation to linear operators-from matrices to bounded linear operatorsin Hilbert space, Taylor and Francis, London, 2001. [8] B.C. Gupta, An extension of Fuglede-Putnam theorem and normality of operators, Indian J. Pure Appl. Math. 14, no. 11. [9] B.C. Gupta and P.B. Ramanujan, On k-quasihyponormal operators-II, Bull. Aust. Math. Soc. 83 (1981), 514–516. [10] P.R. Halmos, A Hilbert space problem book, Springer-Verlag, 1967. [11] J.I. Lee I.H. Jeon and A. Uchiyama, On p-quasihyponormal operators and quasisisimilarity, Math. Inequal. Appl. 6 (2003), 309–315. [12] K. Tanahashi I.H. Jeon, I.H. Kim and A. Uchiyama, Conditions implying self-adjointness of operators, Integral Equations Operator Theory 61 (2008), 549–557. [13] I.H. Jeon and I.H. Kim, On operators satisfying T∗|T2|T ≥ T∗|T|2T∗, Linear Algebra Appl. 418 (2006), 854–862. [14] F. Zuo J.L. Shen and C.S. Yang, On operators satisfying T∗|T2|T ≥ T∗|T∗2|T, Acta Math. Appl. Sin. Engl. Ser. 26 (1976), no. 11, 2109–2116. [15] S.M. Patel K. Tanahashi and A. Uchiyama, On extensions of some Fuglede-Putnam type theorems involving (p, k)-quasihyponormal, spectral, and dominant operators, Math. Nachr. 282 (2009), no. 7, 1022–1032. [16] A.H. Kim and I.H. Kim, Essential spectra of quasisimilar (p, k)-quasihyponormal operators, J. Ineq. Appl. (2006), 1–7. [17] F. Kimura, Analysis of non-normal operators via Aluthge transformation, Integral Equations Operator Theory 50 (1995), no. 3, 375–384. [18] K.B Laursen and M.N Neumann, Introduction to local spectral theory, Clarendon Press, Oxford, 2000. [19] J.W. Lee and I.H. Jeon, A study on operators satisfying |T2| ≥ |T∗|2, Korean J. Math. 19 (2011), no. 1, 61–64. [20] S. Mecheri, Isolated points of spectrum of k-quasi-∗-class A operators, Studia Math. 208 (2012), 87–96. [21] , Fuglede-Putnam theorem for class A operators, Colloq. Math. 138 (2015), no. 2, 183–191. [22] M. Putinar, Quasi-similarity of tuples with Bishop’s property (β), Integral Equation Operator Theory 15 (1992), 1047–1052. [23] M. Radjabalipour, On majorization and normality of operators, Proc. Amer. Math. Soc. 62 (1977), no. 1, 105–110. [24] M.H.M. Rashid, Class wA(s, t) operators and quasisimilarity, Port. Math. 69 (2012), no. 4, 305–320. [25] M.H.M. Rashid, An extension of Fuglede-Putnam theorem for w-hyponormal operators, Afr. Diaspora J. Math. 14 (2012), no. 1, 106—-118. [26]M.H.M. Rashid, Fuglede-Putnam type theorems via the generalized Aluthge transform, Rev. R. Acad. Cienc. Exactas Fıs. Nat. Ser. A Mat. RACSAM 108 (2014), no. 2, 1021—-1034. [27]M.H.M. Rashid, On k-quasi-∗-paranormal operators, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM 110(2016), no. 2, 655–666. [28] M.H.M. Rashid, On quasi-∗-class (A, k) operators, Nonlinear Anal. Forum 22 (2017), no. 1, 45–57. [29] M.H.M. Rashid, Quasinormality and Fuglede-Putnam theorem for (s, p)-w-hyponormal operators, Linear Multilinear Algebra 65 (2017), no. 8, 1600–1616. [30] M.H.M. Rashid, Quasinormality and Fuglede-Putnam theorem for w-hyponormal operators, Thai J. Math. 15 (2017), [31] M.H.M. Rashid, Putnam’s inequality for quasi-∗-class A operators, Acta Math. Acad. Paed. Nyıregyhaziensis 34 (2018), no. 1, 1–10. [32] J.G. Stampfli and B.L. Wadhwa, An asymmetric Fuglede-Putnam theorem for dominant operators, Indiana Univ. Math. J. 25 (1976), 359–365. [33] J.G. Stampfli and B.L. Wadhwa, On dominant operators, Monatsh. Math. 84 (1977), 143–153. [34] K. Takahashi, On the converse of Fuglede-Putnam theorem, Acta Sci. Math. (Szeged) 43 (1981), 123–125. [35] R. Yingbin and Y. Zikun, Spectral structure and subdecomposability of p-hyponormal operators, Proc. Amer. Math. Soc. 128 (1999), 2069–2074. [36] T. Yoshino, Remark on the generalized Fuglede-Putnam theorem, Proc. Amer. Math. Soc. 95 (1985), 571–572. | ||
|
آمار تعداد مشاهده مقاله: 44,340 تعداد دریافت فایل اصل مقاله: 37,705 |
||