Tingley's problem for a Banach space of Lipschitz functions on the closed unit interval (Research on preserver problems on Banach algebras and related topics)

[1] T. Banakh, Every 2-dimensional Banach space has the Mazur-Ulam property, Linear

Algebra Appl., 632 (2022), 268–280.

[2] A. Browder, Introduction to function algebras, W.A. Benjamin, Inc., New YorkAmsterdam, 1969.

[3] L. Cheng and Y. Dong, On a generalized Mazur-Ulam question: extension of isometries

between unit spheres of Banach spaces, J. Math. Anal. Appl., 377 (2011), 464–470.

[4] M. Cueto-Avellaneda, D. Hirota, T. Miura and A.M. Peralta, Exploring new

solutions to Tingley’s problem for function algebras, Quaest. Math., DOI:

10.2989/16073606.2022.2072787.

[5] M. Cueto-Avellaneda, A.M. Peralta, On the Mazur-Ulam property for the space of Hilbertspace-valued continuous functions, J. Math. Anal. Appl., 479 (2019), 875–902.

[6] R.G. Douglas, Banach algebra techniques in operator theory. Second edition, Graduate

Texts in Mathematics 179, Springer-Verlag, New York, 1998.

[7] F.J. Fern´

andez-Polo, J.J. Garc´es, A.M. Peralta, I. Villanueva, Tingley’s problem for spaces

of trace class operators, Linear Algebra Appl., 529 (2017), 294–323.

[8] F.J. Fern´

andez-Polo, E. Jord´

a, A.M. Peralta, Tingley’s problem for p-Schatten von Neumann classes, J. Spectr. Theory, 10 (2020), 809–841.

[9] F.J. Fern´

andez-Polo, A.M. Peralta, On the extension of isometries between the unit

spheres of a C ∗ -algebra and B(H), Trans. Amer. Math. Soc. Ser. B, 5 (2018), 63–80.

[10] F.J. Fern´

andez-Polo, A.M. Peralta, On the extension of isometries between the unit

spheres of von Neumann algebras, J. Math. Anal. Appl., 466 (2018), 127–143.

[11] F.J. Fern´

andez-Polo, A.M. Peralta, Low rank compact operators and Tingley’s problem,

Adv. Math., 338 (2018), 1–40.

[12] F.J. Fern´

andez-Polo, A.M. Peralta, Tingley’s problem through the facial structure of an

atomic JBW ∗ -triple, J. Math. Anal. Appl., 455 (2017), 750–760.

[13] R. Fleming and J. Jamison, Isometries on Banach spaces: function spaces, Chapman &

Hall/CRC Monogr. Surv. Pure Appl. Math. 129, Boca Raton, 2003.

Tingley’s problem for Lip(I)

181

[14] O. Hatori, The Mazur-Ulam property for uniform algebras, Studia Math., 265 (2022),

227–239.

[15] O. Hatori, S. Oi and R. Shindo Togashi, Tingley’s problems on uniform algebras, J. Math.

Anal. Appl., 503 (2021), 125346.

[16] H. Koshimizu, Linear isometries on spaces of continuously differentiable and Lipschitz

continuous functions, Nihonkai Math. J., 22 (2011), 73–90.

[17] C.W. Leung, C.K. Ng, N.C. Wong, Metric preserving bijections between positive spherical

shells of non-commutative Lp -spaces, J. Operator Theory, 80 (2018), 429–452.

[18] C.W. Leung, C.K. Ng, N.C. Wong, On a variant of Tingley’s problem for some function

spaces, J. Math. Anal. Appl., 496 (2021), 124800.

[19] S. Mazur and S. Ulam, Sur les transformationes isom´etriques d’espaces vectoriels norm´es,

C. R. Acad. Sci. Paris 194 (1932), 946–948.

[20] M. Mori, Tingley’s problem through the facial structure of operator algebras, J. Math.

Anal. Appl., 466 (2018), 1281–1298.

[21] M. Mori, N. Ozawa, Mankiewicz’s theorem and the Mazur-Ulam property for C ∗ -algebras,

Studia. Math., 250 (2020), 265–281.

[22] A.M. Peralta, Extending surjective isometries defined on the unit sphere of ℓ∞ (Γ), Rev.

Mat. Complut., 32 (2019), 99–114.

[23] A.M. Peralta, On the unit sphere of positive operators, Banach J. Math. Anal., 13 (2019),

91–112.

[24] A.M. Peralta, R. Tanaka, A solution to Tingley’s problem for isometries between the unit

spheres of compact C ∗ -algebras and JB ∗ -triples, Sci. China Math., 62 (2019), 553–568.

[25] W. Rudin, Real and complex analysis, Third Edition, McGraw-Hill Book. Co., New York,

1987.

[26] D. Tan, X. Huang, R. Liu, Generalized-lush spaces and the Mazur-Ulam property, Studia.

Math., 219 (2013), 139–153.

[27] D. Tan, R. Liu, A note on the Mazur-Ulam property of almost-CL-spaces, J. Math. Anal.

Appl., 405 (2013), 336–341.

[28] R. Tanaka, A further property of spherical isometries, Bull. Aust. Math. Soc., 90 (2014),

304–310.

[29] R. Tanaka, The solution of Tingley’s problem for the operator norm unit sphere of complex

n × n matrices, Linear Algebra Appl., 494 (2016), 274–285.

[30] R. Tanaka, Spherical isometries of finite dimensional C ∗ -algebras, J. Math. Anal. Appl.,

445 (2017), 337–341.

[31] R. Tanaka, Tingley’s problem on finite von Neumann algebras, J. Math. Anal. Appl., 451

(2017), 319–326.

[32] D. Tingley, Isometries of the unit sphere, Geom. Dedicata, 22 (1987), 371–378.

(n)

[33] R. Wang, Isometries of C0 (X), Hokkaido Math. J., 25 (1996), 465–519.

[34] R. Wang and A. Orihara, Isometries on the ℓ1 -sum of C0 (Ω, E) type spaces, J. Math. Sci.

Univ. Tokyo, 2 (1995), 131–154.

...