Two Exercises Concerning the Degree of the Product of Algebraic Numbers
Arturas Dubickas (2005)
Publications de l'Institut Mathématique
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Two Exercises Concerning the Degree of the Product of Algebraic Numbers
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Let L(H) denote the algebra of bounded linear operators on a complex separable and infinite dimensional Hilbert space H. For A, B ∈ L(H), the generalized derivation δ associated with (A, B), is defined by δ(X) = AX - XB for X ∈ L(H). In this note we give some sufficient conditions for A and B under which the intersection between the closure of the range of δ respect to the given topology and the kernel of δ vanishes.