The flip is often discontinuous
نویسنده
چکیده
Let A be a Banach algebra. The flip on A ⊗ A is defined through A ⊗ A ∋ a⊗ b 7→ b⊗ a. If A is ultraprime, El(A), the algebra of all elementary operators on A, can be algebraically identified with A ⊗ A, so that the flip is well defined on El(A). We show that the flip on El(A) is discontinuous if A = K(E) for a reflexive Banach space E with the approximation property.
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ar X iv : m at h / 02 02 30 5 v 1 [ m at h . FA ] 2 8 Fe b 20 02 The flip is often discontinuous
Let A be a Banach algebra. The flip on A ⊗ A is defined through A ⊗ A ∋ a⊗ b 7→ b⊗ a. If A is ultraprime, El(A), the algebra of all elementary operators on A, can be algebraically identified with A ⊗ A, so that the flip is well defined on El(A). We show that the flip on El(A) is discontinuous if A = K(E) for a reflexive Banach space E with the approximation property.
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