Orthograph related to mutual strong Birkhoff–James orthogonality in $$C^*$$-algebras

Arambašić, Lj., Rajić, R.: The Birkhoff–James orthogonality in Hilbert $$C^*$$-modules. Linear Algebra Appl. 437(7), 1913–1929 (2012)

Arambašić, Lj., Rajić, R.: A strong version of the Birkhoff–James orthogonality in Hilbert $$C^*$$-modules. Ann. Funct. Anal. 5(1), 109–120 (2014)

Arambašić, Lj., Rajić, R.: On three concepts of orthogonality in Hilbert $$C^*$$-modules. Linear Multilinear A. 63(7), 1485–1500 (2015)

Arambašić, Lj., Rajić, R.: Operators preserving the strong Birkhoff–James orthogonality on $$\mathbb{B}(H)$$. Linear Algebra Appl. 471, 394–404 (2015)

Arambašić, Lj., Rajić, R.: On symmetry of the (strong) Birkhoff–James orthogonality in Hilbert $$C^*$$-modules. Ann. Funct. Anal. 7(1), 17–23 (2016)

Bakhadly, B.R., Guterman, A.E., Markova, O.V.: Graphs defined by orthogonality. J. Math. Sci. 207, 698–717 (2015)

Bhatia, R., Šemrl, P.: Orthogonality of matrices and some distance problems. Linear Algebra Appl. 287(1–3), 77–85 (1999)

Bhattacharyya, T., Grover, P.: Characterization of Birkhoff–James orthogonality. J. Math. Anal. Appl. 407(2), 350–358 (2013)

Birkhoff, G.: Orthogonality in linear metric spaces. Duke Math. J. 1, 169–172 (1935)

Blackadar, B.: Operator Algebras. Theory of $$C^*$$-algebras and von Neumann Algebras. Encyclopaedia of Mathematical Sciences, vol. 122. Springer, Berlin (2006)

Blanco, A., Turnšek, A.: On maps that preserve orthogonality in normed spaces. Proc. R. Soc. Edinb. Sect. A 136, 709–716 (2006)

Chmieliński, J., Wójcik, P.: Approximate symmetry of Birkhoff orthogonality. J. Math. Anal. Appl. 461(1), 625–640 (2018)

Guterman, A.E., Markova, O.V.: Orthogonality graphs of matrices over skew fields. Zap. Nauchn. Sem. POMI, 463, 81-93 (2017)

English translation: J. Math. Sci. (N. Y.) 232(6), 797-804 (2018)

Halmos, P.R.: Limsups of lats. Indiana Univ. Math. J. 29, 293–311 (1980)

James, R.C.: Orthogonality in normed linear spaces. Duke Math. J. 12, 291–302 (1945)

James, R.C.: Inner products in normed linear spaces. Bull. Am. Math. Soc. 53, 559–566 (1947)

James, R.C.: Orthogonality and linear functionals in normed linear spaces. Trans. Am. Math. Soc. 61, 265–292 (1947)

Kečkić, D.: Orthogonality and smooth points in $$C(K)$$ and $$C_b(\Omega )$$. Eurasian Math. J. 3(4), 44–52 (2012)

Komuro, N., Saito, K.S., Tanaka, R.: On symmetry of Birkhoff orthogonality in the positive cones of $$C^*$$-algebras with applications. J. Math. Anal. Appl. 474(2), 1488–1497 (2019)

Lang, S.: Real and Functional Analysis. Graduate Texts in Mathematics, 3rd edn. Springer, New York (1993)

Magajna, B.: On the distance to finite-dimensional subspaces in operator algebras. J. Lond. Math. Soc. 47(2), 516–532 (1993)

Manuilov, V.M., Troïtsky, E.V.: Hilbert $$C^*$$-Modules. Translations of Mathematical Monographs, vol. 22. American Mathematical Society, Providence (2005)

Moslehian, M.S., Zamani, A.: Characterizations of operator Birkhoff–James orthogonality. Can. Math. Bull. 60(4), 816–829 (2017)

Paul, K., Sain, D., Mal, A., Mandal, K.: Orthogonality of bounded linear operators on complex Banach spaces. Adv. Oper. Theory 3(3), 699–709 (2018)

Stampfli, J.G.: The norm of a derivation. Pac. J. Math. 33, 737–747 (1970)

Turnšek, A.: On operators preserving James’ orthogonality. Linear Algebra Appl. 407, 189–195 (2005)

Zamani, A., Wójcik, P.: Numerical radius orthogonality in $$C^*$$-algebras. Ann. Funct. Anal. (2020). https://doi.org/10.1007/s43034-020-00071-z