Extensions and the Weak Calkin Algebra of Read’s Banach Space Admitting Discontinuous Derivations
نویسنده
چکیده
Read produced the first example of a Banach space ER such that the associated Banach algebra B(ER) of bounded operators admits a discontinuous derivation (J. London Math. Soc. 1989). We generalize the main theorem about B(ER) from which Read deduced this conclusion, as well as the key technical step in his proof, by constructing a strongly split-exact sequence {0} −→ W (ER) −→ B(ER) −→ ←− l2(N) ∼ −→ {0}, where W (ER) denotes the ideal of weakly compact operators on ER, while l2(N) ∼ is the unitization of the Hilbert space l2(N), endowed with the zero product.
منابع مشابه
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