The Operator-Valued Parallelism and Norm-Parallelism in Matrices
Tóm tắt
Let ℌ be a Hilbert space, and let K(ℌ) be the C*-algebra of compact operators on ℌ. In this paper, we present some characterizations of the norm-parallelism for elements of a Hilbert K(ℌ)-module by employing the Birkhoff-James orthogonality. Among other things, we present a characterization of transitive relation of the norm-parallelism for elements in a certain Hilbert K(ℌ)-module. We also give some characterizations of the Schatten p-norms and the operator norm-parallelism for matrices.
Tài liệu tham khảo
Lj. Arambašić and R. Rajić, On symmetry of the (strong) Birkhoff-James orthogonality in Hilbert C*-modules, Ann. Funct. Anal., 7(1) (2016), 17–23.
D. Bakić and B. Guijaš, Hilbert C*-modules over C*-algebras of compact operators, Acta Sci. Math. (Szeged), 68(1–2) (2002), 249–269.
R. Bhatia and P. Semrl, Orthogonality of matrices and some distance problems, Linear Algebra Appl., 287(1–3) (1999), 77–85.
T. Bhattacharyya and P. Grover, Characterization of Birkhoff-James orthogonality, J. Math. Anal. Appl., 407(2) (2013), 350–358.
T. Bottazzi, C. Conde, M. S. Moslehian, P. Wojcik, and A. Zamani, Orthogonality and parallelism of operators on various Banach spaces, J. Aust. Math. Soc., 106(2) (2019), 160–183.
M. Cabrera, J. Martínez, and A. Rodríguez, Hilbert modules revisited: Orthonormal bases and Hilbert-Schmidt operators, Glasgow Math. J., 37 (1995), 45–54.
J. Chmieliński, Remarks on orthogonality preserving mappings in normed spaces and some stability problems, Banach J. Math. Anal., 1(1) (2007), 117–124.
J. Chmieliński, R. Łukasik, and P. Wójcik, On the stability of the orthogonality equation and the orthogonality-preserving property with two unknown functions, Banach J. Math. Anal., 10(4) (2016), 828–847.
P. Ghosh, D. Sain, and K. Paul, On symmetry of Birkhoff-James orthogonality of linear operators, Adv. Oper. Theory, 2(4) (2017), 428–434.
P. Grover, Orthogonality of matrices in the Ky Fan k-norms, Linear Multilinear Algebra, 65(3) (2017), 496–509.
E. C. Lance, Hilbert C*-Modules. A toolkit for operator algebraists, in: London Mathematical Society Lecture Note Series, 210, Cambridge University Press, Cambridge, 1995.
C. K. Li and H. Schneider, Orthogonality of matrices, Linear Algebra App., 81(2) (2003), 175–181.
L. Molnár, Modular bases in a Hilbert A-module, Czechoslovak Math. J., 42(4) (1992), 649–656.
A. Seddik, Rank one operators and norm of elementary operators, Linear Algebra Appl., 424(1) (2007), 177–183.
A. Turnšek, On operators preserving James’ orthogonality, Univ. Beograd. Publ. Elektrotehn. Linear Algebra Appl., 407 (2005), 189–195.
P. Wójcik, Norm-parallelism in classical M-ideals, Indag. Math., 28(2) (2017), 287–293.
A. Zamani, The operator-valued parallelism, Linear Algebra Appl. (N.S.), 505 (2016), 282–295.
A. Zamani and M. S. Moslehian, Exact and approximate operator parallelism, Canad. Math. Bull., 58(1) (2015), 207–224.
A. Zamani and M. S. Moslehian, Norm-parallelism in the geometry of Hilbert C*-modules, Indag. Math. (N.S.), 27(1) (2016), 266–281.