Abstract
We find examples of Ideals in a tridiagonal algebra ALGL∞ and study some properties of Ideals in ALGL∞. We prove the following theorems: Let k and j be fixed natural numbers. Let A be a subalgebra of ALGL∞ and let A2,{k} ⊂ A ⊂ {T ∈ ALGL∞ | T(2k-1,2k) = 0}. Then A is an ideal of ALGL∞ if and only if A = A2,{k} where A2,{k} = {T ∈ ALGL∞ | T(2k-1,2k) = 0, T(2k-1,2k-1) = T(2k,2k) = 0}. Let B be a subalgebra of ALGL∞ such that B2,{j} ⊂ B ⊂ {T ∈ ALGL∞ | T(2j+1,2j) = 0}. Then B is an ideal of ALGL∞ if and only if B = B2,{j}, where B2,{j} = {T ∈ ALGL∞ | T(2j+1,2j) = 0, T(2j,2j) = T(2j+1,2j+1) = 0}.