Möbius gyrovector spaces and functional analysis (Research on preserver problems on Banach algebras and related topics)

[1] Abe, T., Normed gyrolinear spaces: A generalization of normed spaces based on gyrocommutative gyrogroups, Math. Interdiscip. Res. 1 (2016), 143–172.

[2] Abe, T., Complex scalar multiplications on the Poincar´e disk, preprint.

[3] Abe, T. and Hatori, O., Generalized gyrovector spaces and a Mazur-Ulam theorem, Publ.

Math. Debr. 87 (2015), 393–413.

[4] Abe, T. and Watanabe, K., Finitely generated gyrovector subspaces and orthogonal gyrodecomposition in the M¨

obius gyrovector space, J. Math. Anal. Appl. 449 (2017), 77–90.

[5] Frenkel, P.E., On endomorphisms of the Einstein gyrogroup in arbitrary dimension, J.

Math. Phys. 57 (2016), 032301, 3 pp.

[6] Ferreira, M. and Ren, G., M¨

obius gyrogroups: A Clifford algebra approach, J. Algebra

328 (2011), 230–253.

[7] Ferreira, M. and Suksumran, T., Orthogonal gyrodecompositions of real inner product

gyrogroups, Symmetry 2020, 12(6), 941.

[8] Goebel, K. and Reich, S., Uniform Convexity, Hyperbolic Geometry, and Nonexpansive

Mappings, Marcel Dekker, New York, 1984.

[9] Harris, L.A., Schwarz-Pick systems of pseudometrics for domains in normed linear spaces,

Advances in Holomorphy, North Holland, Amsterdam, 1979, pp.345–406.

[10] Hatori, O., Examples and applications of generalized gyrovector spaces, Results Math. 71

(2017), 295–317.

[11] Honma, T. and Hatori, O., A gyrogeometric mean in the Einstein gyrogroup, Symmetry

2020, 12(8), 1333.

[12] Moln´

ar, L. and Virosztek, D., On algebraic endomorphisms of the Einstein gyrogroup, J.

Math. Phys. 56 (2015), 082302, 5 pp.

[13] Rudin, W., Function Theory in the Unit Ball of Cn , Springer-Verlag, New York, 1980.

[14] Suksumran, T. and Wiboonton, K., Einstein gyrogroup as a B-loop, Rep. Math. Phys. 76

(2015), 63–74.

[15] Ungar, A.A., The abstract complex Lorentz transformation group with real metric. I.

Special relativity formalism to deal with the holomorphic automorphism group of the unit

ball in any complex Hilbert space, J. Math. Phys. 35 (1994), 1408–1426.

[16] Ungar, A.A., Analytic Hyperbolic Geometry and Albert Einstein’s Special Theory of Relativity, World Scientific Publishing Co. Pte. Ltd., Singapore, 2008.

[17] Watanabe, K., A confirmation by hand calculation that the M¨

obius ball is a gyrovector

space, Nihonkai Math. J. 27 (2016), 99–115.

[18] Watanabe, K., Orthogonal gyroexpansion in M¨

obius gyrovector spaces, J. Funct. Spaces

2017, Article ID 1518254, 13 pp.

[19] Watanabe, K., A Cauchy type inequality for M¨

obius operations, J. Inequal. Appl. 2018,

Paper No. 97, 9 pp.

[20] Watanabe, K., A Cauchy-Bunyakovsky-Schwarz type inequality related to the M¨

obius

addition, J. Math. Inequal. 12 (2018), 989–996.

[21] Watanabe, K., Cauchy-Bunyakovsky-Schwarz type inequalities related to M¨

obius operations, J. Inequal. Appl. 2019, Paper No. 179, 19 pp.

[22] Watanabe, K., Continuous quasi gyrolinear functionals on M¨

obius gyrovector spaces, J.

Funct. Spaces 2020, Article ID 1950727, 14 pp.

[23] Watanabe, K., On quasi gyrolinear maps between M¨

obius gyrovector spaces induced from

finite matrices, Symmetry 2021, 13(1), 76.

¨ bius gyrovector spaces and functional analysis

Mo

237

[24] Watanabe, K., On Lipschitz continuity with respect to the Poincar´e metric of linear contractions between M¨

obius gyrovector spaces, J. Inequal. Appl. 2021, Paper No. 166, 15

pp.

[25] Watanabe, K., On a notion of complex M¨

obius gyrovector spaces, Nihonkai Math. J. 32

(2021), 111–131.

[26] Watanabe, K., On inner product gyrovector spaces, preprint.

[27] Watanabe, K., Quasi gyrolinear mappings between inner product gyrovector spaces,

preprint.

[28] Watanabe, K., On the Lipschitz continuity of contractive linear operators with respect

to the M¨

obius metric (Japanese), manuscript for Proceedings of Conference on Function

Algebras 2021.

...