논문KCI 등재
LIE IDEALS IN TRIDIAGONAL ALGEBRA ALGL∞
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초록
We give examples of Lie ideals in a tridiagonal algebra AlgL∞ and study some properties of Lie ideals in AlgL∞. We also investigate relationships between Lie ideals in AlgL∞. Let k be a fixed natural number. Let A be a linear manifold in AlgL∞ such that T(2k−1,2k) = 0 for all T ∈ A. Then A is a Lie ideal if and only if T(2k−1,2k−1) = T(2k,2k) for all T ∈ A.
Abstract
We give examples of Lie ideals in a tridiagonal algebra AlgL∞ and study some properties of Lie ideals in AlgL∞. We also investigate relationships between Lie ideals in AlgL∞. Let k be a fixed natural number. Let A be a linear manifold in AlgL∞ such that T(2k−1,2k) = 0 for all T ∈ A. Then A is a Lie ideal if and only if T(2k−1,2k−1) = T(2k,2k) for all T ∈ A.
참고문헌 (5)
- C. K. Fong, "Lie and Jordan ideals of operators on Hilbert spaces", Proc. Amer. Math. Soc, 84(4), pp.516~520 (1982)
- A. Hopenwasser, "Lie ideal in operator algebras", J. Operator Theory, 52(2), pp.325~340 (2004)
- T. D. Hudson, "Lie ideal in triangular operator algebras", Trans. Amer. Math. Soc, 350(8), pp.3321~3339 (1998)
- Y. S. Jo, "Isometries of tridiagonal algebras", Pacific J. Math, 140(1), pp.97~115 (1989)
- Y. S. Jo, "Isomorphisms of AlgLn and AlgL∞", Michigan Math. J, 37(2), pp.305~314 (1990)
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