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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.
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참고문헌 (5)
참고문헌 신청
A. Hopenwasser / 2004 / Lie ideal in operator algebras / J. Operator Theory 52 (2) : 325 ~ 340
C. K. Fong / 1982 / Lie and Jordan ideals of operators on Hilbert spaces / Proc. Amer. Math. Soc 84 (4) : 516 ~ 520
T. D. Hudson / 1998 / Lie ideal in triangular operator algebras / Trans. Amer. Math. Soc 350 (8) : 3321 ~ 3339
Y. S. Jo / 1989 / Isometries of tridiagonal algebras / Pacific J. Math 140 (1) : 97 ~ 115
Y. S. Jo / 1990 / Isomorphisms of AlgLn and AlgL∞ / Michigan Math. J 37 (2) : 305 ~ 314
C. K. Fong / 1982 / Lie and Jordan ideals of operators on Hilbert spaces / Proc. Amer. Math. Soc 84 (4) : 516 ~ 520
T. D. Hudson / 1998 / Lie ideal in triangular operator algebras / Trans. Amer. Math. Soc 350 (8) : 3321 ~ 3339
Y. S. Jo / 1989 / Isometries of tridiagonal algebras / Pacific J. Math 140 (1) : 97 ~ 115
Y. S. Jo / 1990 / Isomorphisms of AlgLn and AlgL∞ / Michigan Math. J 37 (2) : 305 ~ 314
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