A note on Bicomplex Linear operators on bicomplex Hilbert spaces

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2016 by IJMTT Journal
Volume-36 Number-3
Year of Publication : 2016
Authors : Khalid Manzoor
  10.14445/22315373/IJMTT-V36P530

MLA

Khalid Manzoor "A note on Bicomplex Linear operators on bicomplex Hilbert spaces", International Journal of Mathematics Trends and Technology (IJMTT). V36(3)218-224 August 2016. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
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.

References
[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.

Keywords
Bicomplex numbers, hyperbolic norm, bicomplex isomerty.