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 $\small{T_{(2k-1,2k)}=0}$ for all $\small{T{\in}\mathcal{A}}$. Then $\small{\mathcal{A}}$ is a Lie ideal if and only if $\small{T_{(2k-1,2k-1)}=T_{(2k,2k)}}$ for all $\small{T{\in}\mathcal{A}}$.
Keywords
linear manifold;Lie ideal;tridiagonal algebras;
Language
English
Cited by
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.