본문 바로가기
KERD
논문KCI 등재

Some properties of bilinear mappings on the tensor product of $C^*$-algebras

Vishnu Narayan Mishra|Nilakshi Goswami|Anamika Sarma
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2019.12|한국수학논문집 (Korean Journal of Mathematics)|제27권 제4호|pp. 977-1003

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

bilinear map$C^*$-algebratensor productcentralizerorthogonal complement
주제분류수학

초록

Let $\mathcal{A}$ and $\mathcal{B}$ be two unital $C^*$-algebras and $\mathcal{A}\otimes\mathcal{B}$ be their algebraic tensor product. For two bilinear maps on $\mathcal{A}$ and $\mathcal{B}$ with some specific conditions, we derive a bilinear map on $\mathcal{A}\otimes\mathcal{B}$ and study some characteristics. Considering two $\mathcal{A}\otimes\mathcal{B}$ bimodules, a centralizer is also obtained for $\mathcal{A}\otimes\mathcal{B}$ corresponding to the given bilinear maps on $\mathcal{A}$ and $\mathcal{B}$. A relationship between orthogonal complements of subspaces of $\mathcal{A}$ and $\mathcal{B}$ and their tensor product is also deduced with suitable example.

Abstract

Let $\mathcal{A}$ and $\mathcal{B}$ be two unital $C^*$-algebras and $\mathcal{A}\otimes\mathcal{B}$ be their algebraic tensor product. For two bilinear maps on $\mathcal{A}$ and $\mathcal{B}$ with some specific conditions, we derive a bilinear map on $\mathcal{A}\otimes\mathcal{B}$ and study some characteristics. Considering two $\mathcal{A}\otimes\mathcal{B}$ bimodules, a centralizer is also obtained for $\mathcal{A}\otimes\mathcal{B}$ corresponding to the given bilinear maps on $\mathcal{A}$ and $\mathcal{B}$. A relationship between orthogonal complements of subspaces of $\mathcal{A}$ and $\mathcal{B}$ and their tensor product is also deduced with suitable example.

참고문헌 (34)

  1. C. A. Akemann, "Multipliers of C*-algebras", J. Funct. Anal, 13, pp.277~301 (1973)
  2. A. Alahamdi, "A characterization of Jordan left *-centralizers in rings with involution", Appl. Math. Inf. Sci, 11(2), pp.441~447 (2017)
  3. D. P. Blecher, "Geometry of the tensor product of C*-algebras", Math. Proc. Cam-bridgePhilos. Soc, pp.119~127 (1988)
  4. F. F. Bonsall, "Complete normed Algebras" (1973), Springer- Verlag
  5. M. F. Bruckler, "Tensor products of C*-algebras, Operator spaces and Hilbert Cꠗ-modules", Math. comm, 4, pp.257~268 (1999)
  6. T. K. Carne, "Tensor products and Banach algebras", J. London Math. Soc, 17(2), pp.480~488 (1978)
  7. DIPANKAR DAS, "Some fixed point results for operator pairs in C^*-algebra valued modular b -metric spaces via Class functions with applications", Advanced Studies in Contemporary Mathematics, 29(3), pp.383~400 (2019), 장전수학회
  8. D. Das, "Some xed point theorems on the sum and product of operators in tensor product spaces", IJPAM, 10D(3), pp.651~663 (2016)
  9. D. Das, "Some results on xed point theorems in Banach algebras", International Journal of Analysis and Applications, 13(1), pp.32~40 (2017)
  10. D. Das, "Some results on the projective cone normed tensor product spaces over Banach algebras", Bol. Soc. Paran. Mat, 38(1), pp.197~221 (2020)
  11. Deepmala, "A Study on Fixed Point Theorems for Nonlinear Contractions and its Applications", Ph.D., pp.2014
  12. Deepmala, "A study on some problems on existence of solutions for nonlinear functional-integral equations", Acta Mathematica Scientia, 33B(5), pp.1305~1313 (2013)
  13. M. Gagne, "Applications of Bilinear maps in Cryptography. UWSpace", M.sc, pp.2002
  14. H. Ghahramani, "On centralizers of Banach algebras", The Bull. of the Malaysian Math. Soc. Series, 38(1), pp.155~164 (2015)
  15. N. Goswami, "On a subset of invertible elements of C*-algebras and some related xed point theorems", Journal of Tripura Math. Soc., 19, pp.21~37 (2017)
  16. A. Guichardet, "Tensor products of C*-algebras", pp.1969
  17. S. Helgason, "Multipliers of Banach algebras", Ann. of Math., 64, pp.240~254 (1956)
  18. B. E. Johnson, "An introduction to the theory of centralizers", Proc. London Math. Soc., 14, pp.299~320 (1964)
  19. A. S. Kavruk, "Complete positivity in opeartor algebras", M.Sc., pp.2006
  20. S. Kaijser, "Projective tensor products of C*-algebras", Math. Scand, 65, pp.161~187 (1984)
  21. X. Liu, "Common xed point theorem of six self-mappings in Menger spaces using (CLRST ) property", Open Mathematics, 16, pp.1423~1434 (2018)
  22. Lakshmi Narayan Mishra, "On the concept of existence and local attractivity of solutions for some quadratic Volterra integral equation of fractional order", Applied Mathematics and Computation, 285, pp.174~183 (2016), Elsevier BV[DOI]
  23. L. N. Mishra, "On existence and behavior of solutions to some nonlinear inte-gral equations with applications", Ph.D., pp.2017
  24. L. N. Mishra, "Fixed point theorems with digital contractions image processing", Nonlinear Sci. Lett. A, 9(2), pp.104~115 (2018)
  25. L. N. Mishra, "Unique Fixed Point The-orems for Generalized Contractive Mappings in Partial Metric Spaces", Journal of Function Spaces, 2015, pp.8~ (2015)
  26. L. N. Mishra, "Fixed point theorems for general-ized weakly S-contractive mappings in partial metric spaces", Journal of Applied Analysis and Computation, 5(4), pp.600~612 (2015)[DOI]
  27. N. M. McCullagh, "Cryptographic Applications of Bilinear Maps", Ph.D., pp.2005
  28. H. K. Pathak, "Common xed point theorems for PD-operator pairs under Relaxed conditions with applications", Journal of Computational and Applied Mathematics, 239, pp.103~113 (2013)
  29. A. R. Raymond, "Introduction to Tensor products of Banach Spaces" (2001), Springer - Verlag
  30. A. Sarma, "Some results on positive elements in the tensor product of C*-algebras", Int. J. Math. Trends and Technology, 51(3), pp.237~243 (2017)
  31. M. S. T. EI-Sayiad, "A note on Jordan left *-centralizers on prime and semiprime rings with involution", J. Taibah Univ. Sci., pp.1080~1082 (2018)
  32. "Notes on Tensor products" (2014)[URL]
  33. "Introduction to bilinear forms" (2014)[URL]
  34. T. Turumaru, "On the direct product of operator algebras I", Tohoku Math. Journ., 4, pp.242~251 (1952)

관련 논문AI추천

Triple centralizers of C*-algebrasHamid Reza Moradi, Mohsen Erfanian Omidvar, Seyed Mohammad Davarpanah강원경기수학회 · 한국수학논문집2018 · 제26권 제4호MAPS PRESERVING η-PRODUCT A*B + ηBA* ON C*-ALGEBRASAli Taghavi, Haji Mohammad Nazari, Hamid Rohi, Vahid Darvish대한수학회 · 대한수학회지2017 · 제54권 제3호ON THE EXTENDED HAAGERUP TENSOR PRODUCT IN OPERATOR SPACESMasaru Nagisa, Takashi Itoh대한수학회 · 대한수학회지2014 · 제51권 제2호On χ⊗η-Strong Connes Amenability of Certain Dual Banach AlgebrasAli Ghaffari, Ebrahim Tamimi한국수학교육학회 · 이론수학과 교직수학2024 · 제31권 제1호Nonlinear maps preserving the mixed product $_*[X\diamond Y, Z]$ on $*$-algebrasAbbas Hussain Shikeh, Mohammad Aslam Siddeeque, Raof Ahmad Bhat대한수학회 · 대한수학회논문집2023 · 제38권 제4호Representations of $C^{\ast}$-ternary ringsAjay Kumar, Arpit Kansal, Vandana Rajpal대한수학회 · 대한수학회논문집2023 · 제38권 제1호

이 간행물의 다른 논문 (18건)

Optimal radiocoloring of treesXiaoling Zhangpp. 831-841Some new estimates for exponentially $(\hbar,\mathfrak{m})$-convex functions via extended generalized fractional integral operatorsSaima Rashid, Khalida Inayat Noor, Muhammad Aslam Noorpp. 843-860Fixed point theorems for asymptotically regular mappings in fuzzy metric spacesBijoy Patir, Nilakshi Goswamipp. 861-877On numerical range and numerical radius of convex function operatorsKhaoula Zaiz, Abdelouahab Mansourpp. 879-898Some growth aspects of special type of differential polynomial generated by entire and meromorphic functions on the basis of their relative $\left( p,q\right) $-th ordersTanmay Biswaspp. 899-927
원문 보기