Abstract
We present criteria and related techniques which help to decide whether the adjoint operator ideal (𝔄*, A*) of an injective and totally accessible maximal Banach ideal (𝔄, A) is itself also totally accessible. This approach (which involves the transfer of the principle of local reflexivity to operator ideals) is based on the extension of finite rank operators, viewed as elements of the adjoint ideal (𝔄*, A*). Using the local properties (I) and (S) of the corresponding product ideal 𝔄* ∘ 𝔏∞, these methods even enable us to show that 𝔏∞ and 𝔏1 cannot be totally accessible – answering an open question of Defant and Floret.
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