Title:
|
Numerical radius inequalities for Hilbert $C^{*}$-modules (English) |
Author:
|
Fakri Moghaddam, Sadaf |
Author:
|
Kamel Mirmostafaee, Alireza |
Language:
|
English |
Journal:
|
Mathematica Bohemica |
ISSN:
|
0862-7959 (print) |
ISSN:
|
2464-7136 (online) |
Volume:
|
147 |
Issue:
|
4 |
Year:
|
2022 |
Pages:
|
547-566 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
We present a new method for studying the numerical radius of bounded operators on Hilbert $C^*$-modules. Our method enables us to obtain some new results and generalize some known theorems for bounded operators on Hilbert spaces to bounded adjointable operators on Hilbert $C^*$-module spaces. (English) |
Keyword:
|
numerical radius |
Keyword:
|
inner product space |
Keyword:
|
$C^*$-algebra |
MSC:
|
46C05 |
MSC:
|
47A12 |
MSC:
|
47C10 |
idZBL:
|
Zbl 07655826 |
idMR:
|
MR4512173 |
DOI:
|
10.21136/MB.2022.0066-21 |
. |
Date available:
|
2022-11-16T11:19:02Z |
Last updated:
|
2023-04-11 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151098 |
. |
Reference:
|
[1] Bhunia, P., Bag, S., Paul, K.: Numerical radius inequalities and its applications in estimation of zeros of polynomials.Linear Algebra Appl. 573 (2019), 166-177. Zbl 07060568, MR 3933295, 10.1016/j.laa.2019.03.017 |
Reference:
|
[2] Dragomir, S. S.: Some refinements of Schwarz inequality.Proceedings of the Simpozionul de Matematici si Aplicatii, Timisoara, Romania (1985), 13-16. |
Reference:
|
[3] Dragomir, S. S.: A survey of some recent inequalities for the norm and numerical radius of operators in Hilbert spaces.Banach J. Math. Anal. 1 (2007), 154-175. Zbl 1136.47006, MR 2366098, 10.15352/bjma/1240336213 |
Reference:
|
[4] Dragomir, S. S.: Inequalities for the norm and numerical radius of composite operator in Hilbert spaces.Inequalities and Applications International Series of Numerical Mathematics 157. Birkhäuser, Basel (2009), 135-146. Zbl 1266.26036, MR 2758975, 10.1007/978-3-7643-8773-0_13 |
Reference:
|
[5] Dragomir, S. S.: Power inequalities for the numerical radius of a product of two operators in Hilbert spaces.Sarajevo J. Math. 5 (2009), 269-278. Zbl 1225.47008, MR 2567758 |
Reference:
|
[6] Goldberg, M., Tadmor, E.: On the numerical radius and its applications.Linear Algebra Appl. 42 (1982), 263-284. Zbl 0479.47002, MR 0656430, 10.1016/0024-3795(82)90155-0 |
Reference:
|
[7] Goldstein, A. A., Ryff, J. V., Clarke, L. E.: Problems and solutions: Solutions of advanced problems 5473.Am. Math. Mon. 75 (1968), 309-310. MR 1534789, 10.2307/2314992 |
Reference:
|
[8] Gustafson, K. E., Rao, D. K. M.: Numerical Range: The Field of Values of Linear Operators and Matrices.Universitext. Springer, New York (1997). Zbl 0874.47003, MR 1417493, 10.1007/978-1-4613-8498-4 |
Reference:
|
[9] Hardy, G. H., Littlewood, J. E., Pólya, G.: Inequalities.Cambridge Mathematical Library. Cambridge University Press, Cambridge (1988). Zbl 0634.26008, MR 0944909 |
Reference:
|
[10] Hosseini, M. S., Omidvar, M. E., Moosavi, B., Moradi, H. R.: Some inequalities for the numerical radius for Hilbert $C^*$-modules space operators.Georgian Math. J. 28 (2021), 255-260. Zbl 07339609, MR 4235824, 10.1515/gmj-2019-2053 |
Reference:
|
[11] Kadison, R. V., Ringrose, J. R.: Fundamentals of the Theory of Operator Algebras. Vol. 1. Elementary Theory.Pure and Applied Mathematics 100. Academic Press, New York (1983). Zbl 0518.46046, MR 0719020 |
Reference:
|
[12] Kaplansky, I.: Modules over operator algebras.Am. J. Math. 75 (1953), 839-858. Zbl 0051.09101, MR 0058137, 10.2307/2372552 |
Reference:
|
[13] Kittaneh, F.: Notes on some inequalities for Hilbert space operators.Publ. Res. Inst. Math. Sci. 24 (1988), 283-293. Zbl 0655.47009, MR 0944864, 10.2977/prims/1195175202 |
Reference:
|
[14] Kittaneh, F.: Numerical radius inequalities for Hilbert space operators.Stud. Math. 168 (2005), 73-80. Zbl 1072.47004, MR 2133388, 10.4064/sm168-1-5 |
Reference:
|
[15] Lance, E. C.: Hilbert $C^*$-Module: A Toolkit for Operator Algebraists.London Mathematical Society Lecture Note Series 210. Cambridge University Press, Cambridge (1995). Zbl 0822.46080, MR 1325694, 10.1017/CBO9780511526206 |
Reference:
|
[16] McCarthy, C. A.: $C_p$.Isr. J. Math. 5 (1967), 249-271. Zbl 0156.37902, MR 0225140, 10.1007/BF02771613 |
Reference:
|
[17] Mehrazin, M., Amyari, M., Omidvar, M. E.: A new type of numerical radius of operators on Hilbert $C^*$-module.Rend. Circ. Mat. Palermo (2) 69 (2020), 29-37. Zbl 07193605, MR 4148774, 10.1007/s12215-018-0385-3 |
Reference:
|
[18] Mirmostafaee, A. K., Rahpeyma, O. P., Omidvar, M. E.: Numerical radius ineqalities for finite sums of operators.Demonstr. Math. 47 (2014), 963-970. Zbl 1304.47007, MR 3290398, 10.2478/dema-2014-0076 |
Reference:
|
[19] Moosavi, B., Hosseini, M. S.: Some inequalities for the numerical radius for operators in Hilbert $C^*$-modules space.J. Inequal. Spec. Funct. 10 (2019), 77-84. MR 4016178 |
Reference:
|
[20] Murphy, G. J.: $C^*$-Algebras and Operator Theory.Academic Press, Boston (1990). Zbl 0714.46041, MR 1074574 |
Reference:
|
[21] Paschke, W. L.: Inner product modules over $B^*$-algebras.Trans. Am. Math. Soc. 182 (1973), 443-468. Zbl 0239.46062, MR 0355613, 10.1090/S0002-9947-1973-0355613-0 |
Reference:
|
[22] Rieffel, M. A.: Induced representations of $C^*$-algebras.Adv. Math. 13 (1974), 176-257. Zbl 0284.46040, MR 0353003, 10.1016/0001-8708(74)90068-1 |
Reference:
|
[23] Sattari, M., Moslehian, M. S., Yamazaki, T.: Some generalized numerical radius ineqalities for Hilbert space operators.Linear Algebra Appl. 470 (2015), 216-227. Zbl 1322.47010, MR 3314313, 10.1016/j.laa.2014.08.003 |
Reference:
|
[24] Yamazaki, T.: On upper and lower bounds of the numerical radius and an equality condition.Stud. Math. 178 (2007), 83-89. Zbl 1114.47003, MR 2282491, 10.4064/sm178-1-5 |
. |