Joint \(n\)-normality of linear transformations
Authors
A. A. AL-Dohiman
- Mathematical Analysis and Applications, Mathematics Department, College of Science, Jouf University, P.O. Box 2014, Sakaka, Saudi Arabia.
Abstract
This paper is concerned with studying a new class of multivariable operators know as joint \(n\)-normal \(q\)-tuple of operators.
Some structural properties of some members of this class are given.
Share and Cite
ISRP Style
A. A. AL-Dohiman, Joint \(n\)-normality of linear transformations, Journal of Mathematics and Computer Science, 25 (2022), no. 4, 361--369
AMA Style
AL-Dohiman A. A., Joint \(n\)-normality of linear transformations. J Math Comput SCI-JM. (2022); 25(4):361--369
Chicago/Turabian Style
AL-Dohiman, A. A.. "Joint \(n\)-normality of linear transformations." Journal of Mathematics and Computer Science, 25, no. 4 (2022): 361--369
Keywords
- \(n\)-normal
- joint \(n\)-normal
- tensor product
MSC
References
-
[1]
E. H. Abood, M. A. Al-loz, On some generalizations of $(n,m)$-normal powers operators on Hilbert space, J. Progress. Res. Math., 7 (1978), 113--114
-
[2]
E. H. Abood, M. A. Al-loz, On some generalization of normal operators on Hilbert space, Iraqi J. Sci., 56 (2015), 1786--1794
-
[3]
S. A. O. Ahmed Mahmoud, On the joint class of $(m, q)$-partial isometries and the joint $m$-invertible tuples of commuting operators on a Hilbert space, Ital. J. Pure Appl. Math., 40 (2018), 438--463
-
[4]
S. A. O. Ahmed Mahmoud, M. Chō, J. E. Lee, On $(m,C)$-Isometric Commuting Tuples of Operators on a Hilbert Space, Results Math., 73 (2018), 31 pages
-
[5]
S. A. O. Ahmed Mahmoud, O. B. Sid Ahmed, On the classes of $(n, m)$-power $D$-normal and $(n,m)$-power $D$-quasi-normal operators, Oper. Matrices, 13 (2019), 705--732
-
[6]
S. A. Alzuraiqi, A. B. Patel, On $n$-Normal Operators, General Math. Notes, 1 (2020), 61--73
-
[7]
M. Chō, S. A. O. Ahmed Mahmoud, $(A,m)$-Symmetric commuting tuple of operators on a Hilbert space, J. Inequalities Appl., 22 (2019), 12 pages
-
[8]
M. Chō, E. M. O. Beiba, S. A. O. Ahmed Mahmoud, $(n_1,\cdots, n_p)$-quasi-$m$-isometric commuting tuple of operators on a Hilbert space, Ann. Funct. Anal., 12 (2021), 1--18
-
[9]
M. Chō, J. E. Lee, K. Tanahashic, A. Uchiyamad, Remarks on $n$-normal Operators, Filomat, 32 (2018), 5441--5451
-
[10]
M. Chō, B. N. Načevska, Spectral properties of $n$-normal operators, Filomat, 3 (2018), 5063--5069
-
[11]
R. E. Curto, S. H. Lee, J. Yoon, $k$-Hyponormality of multivariable weighted shifts, J. Funct. Anal., 229 (2005), 462--480
-
[12]
R. E. Curto, S. H. Lee, J. Yoon, Hyponormality and subnormality for powers of commuting pairs of subnormal operators, J. Funct. Anal., 245 (2007), 390--412
-
[13]
D. S. Djordjević, M. Chō, D. Mosić, Polynomially normal operators, J. Funct. Anal., 11 (2020), 493--504
-
[14]
J. Gleason, S. Richter, $m$-Isometric Commuting Tuples of Operators on a Hilbert Space, Integral Equations Operator Theory, 56 (2006), 181--196
-
[15]
M. Guesba, E. M. O. Beiba, S. A. O. Ahmed Mahmoud, Joint $A$-hyponormality of operators in semi-Hilbert spaces, Linear and Multilinear Algebra, 67 (2019), 20 pages
-
[16]
P. H. W. Hoffmann, M. Mackey, $(m, p)$-isometric and $(m, \infty)$-isometric operator tuples on normed spaces, Asian-Eur. J. Math., 8 (2015), 32 pages
-
[17]
A. A. S. Jibril, On $n$-Power Normal Operators, Arab. J. Sci. Eng. Sect. A Sci., 33 (2008), 247--251
-
[18]
I. Kaplansky, Products of normal operators, Duke Math. J., 20 (1953), 257--260
-
[19]
J. Stochel, Seminormality of operators from their tensor product, Proc. Amer. Math. Soc., 124 (1996), 135--140
