International Journal of Mathematics Trends and Technology
Volume 36 | Number 3 | Year 2016 | Article Id. IJMTT-V36P530 | DOI : https://doi.org/10.14445/22315373/IJMTT-V36P530
In this paper we define the isomorphism between the bicomplex Hilbert spaces. We also give some simple and basic results on bicomplex isomorphism with respect to hyperbolic-valued norm on the bicomplex Hilbert spaces.
[1] D. Alpay, M. E. Lunna-Elizarrarars, M. Shapiro and D. C. Struppa, Basics of Functional Analysis with Bicomplex scalars and Bicomplex Schur Analysis, Springer Briefs in Mathematic, 2014.
[2] F. Colombo, I. Sabadin and D. C. Struppa, Bicomplex holomorphic functional calculus, Math. Nachr. 287, No. 13 (2013), 1093-1105.
[3] F. Colombo, I. Sabadin, D. C. Struppa, A. Vajiac and M. B. Vajiac, Singularities of functions of one and several bicomplex variables, Ark. Mat. 49, (2011), 277-294.
[4] J. B. Conway, A course in Functional Analysis, 2nd Edition, Springer. Berlin, 1990.
[5] C. C. Cowen and B. D. MacCluer, Composition operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, 1995.
[6] R. Gervais Lavoie, L. Marchildon and D. Rochon, Infinite-dimensional bicomplex Hilbert spaces, Ann. Funct. Anal, 1, No. 2 (2010), 75-91.
[7] R. Gervais Lavoie, L. Marchildon and D. Rochon, Finite-dimensional bicomplex Hilbert spaces, Adv. Appl. Clifford Algebr. 21, No.3 (2011), 561-581.
[8] R. Kumar, R. Kumar and D. Rochon, The fundamental theorems in the framework of bicomplex topological modules,(2011), arXiv:1109.3424v1.
[9] R. Kumar, K. Singh, Bicomplex linear operators on bicomplex Hilbert spaces and Littlewood’s subordination theorem, Adv. Appl. Clifford Algebras, 25, (2015), 591-610.
[10] Romesh Kumar, Kulbir Singh, Heera Saini, Sanjay Kumar, Bicomplex Weighted Hardy spaces and Bicomplex C-algebras, Adv. Appl. Clifford Algebras 26, (2016), 217-235.
[11] M. E. Lunna-Elizarrarars, C. O. Perez-Regalado and M. Shapiro, On linear functionals and Hahn-Banach theorems for hyperbolic and bicomplex modules, Adv. Appl. Clifford Algebr. 24, (2014), 1105-1129.
[12] M. E. Lunna-Elizarrarars, C. O. Perez-Regalado and M. Shapiro, On the bicomplex Gleason-Kahane Zelazko Theorem, Complex Anal. Oper. Theory, 10, No. 2 (2016), 327-352.
[13] M. E. Lunna-Elizarrarars, M. Shapiro and D. C. Struppa, On Clifford analysis for holomorphic mappings, Adv. Geom. 14, No. 3 (2014), 413-426.
[14] M. E. Lunna-Elizarrarars, M. Shapiro, D. C. Struppa and A. Vajiac, Bicomplex numbers and their elementary functions, Cubo 14, No. 2 (2012), 61-80.
[15] G. B. Price, An introduction to Multicomplex Spaces and Functions, 3rd Edition, Marcel Dekker, New York, 1991.
[16] D. Rochon and M. Shapiro, On algebraic properties of bicomplex and hyperbolic numbers, Anal. Univ. Oradea, Fasc. Math. 11 (2004), 71- 110.
[17] D. Rochon and S. Tremblay, Bicomplex Quantum Mechanics II: The Hilbert space, Advances in Applied Clifford Algebras, 16 No. 2 (2006), 135-157.
[18] J. H. Shapiro, Composition Operators and Classical Function Theory, Springer-Verlag, New-York, 1993.
Khalid Manzoor, "A note on Bicomplex Linear operators on bicomplex Hilbert spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 36, no. 3, pp. 218-224, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V36P530
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