LIE IDEALS IN TRIDIAGONAL ALGEBRA ALG𝓛

Title & Authors
LIE IDEALS IN TRIDIAGONAL ALGEBRA ALG𝓛
Kang, Joo Ho;

Abstract
We give examples of Lie ideals in a tridiagonal algebra $\small{Alg\mathcal{L}_{\infty}}$ and study some properties of Lie ideals in $\small{Alg\mathcal{L}_{\infty}}$. We also investigate relationships between Lie ideals in $\small{Alg\mathcal{L}_{\infty}}$. Let k be a fixed natural number. Let $\small{\mathcal{A}}$ be a linear manifold in $\small{Alg\mathcal{L}_{\infty}}$ such that $T_{(2k-1,2k)} Keywords linear manifold;Lie ideal;tridiagonal algebras; Language English Cited by 1. IDEALS IN A TRIDIAGONAL ALGEBRA ALGL,;; Journal of applied mathematics & informatics, 2016. vol.34. 3_4, pp.257-267 1. IDEALS IN A TRIDIAGONAL ALGEBRA ALGL∞, Journal of applied mathematics & informatics, 2016, 34, 3_4, 257 References 1. C. K. Fong, C. R. Miers, and A. R. Sourour, Lie and Jordan ideals of operators on Hilbert spaces, Proc. Amer. Math. Soc. 84 (1982), no. 4, 516-520. 2. A. Hopenwasser and V. Paulsen, Lie ideal in operator algebras, J. Operator Theory 52 (2004), no. 2, 325-340. 3. T. D. Hudson, L. W. Marcoux, and A. R. Sourour, Lie ideal in triangular operator algebras, Trans. Amer. Math. Soc. 350 (1998), no. 8, 3321-3339. 4. Y. S. Jo, Isometries of tridiagonal algebras, Pacific J. Math. 140 (1989), no. 1, 97-115. 5. Y. S. Jo and T. Y. Choi, Isomorphisms of$AlgL_n$and$AlgL_{\infty}\$, Michigan Math. J. 37 (1990), no. 2, 305-314.