Accepted author manuscript, 320 KB, PDF document
Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Extensions and the weak Calkin algebra of Read's Banach space admitting discontinuous derivations
AU - Laustsen, Niels Jakob
AU - Skillicorn, Richard
PY - 2016/11/10
Y1 - 2016/11/10
N2 - Read produced the first example of a Banach space E such that the associated Banach algebra B(E) of bounded operators admits a discontinuous derivation (J. London Math. Soc. 1989). We generalize Read's main theorem about B(E) from which he deduced this conclusion, as well as the key technical lemmas that his proof relied on, by constructing a strongly split-exact sequence{0}→W(E)→B(E)→l2~→{0}, W(E) where W(E) denotes the ideal of weakly compact operators on E, while l2~ is the unitization of the Hilbert space l2, endowed with the zero product.
AB - Read produced the first example of a Banach space E such that the associated Banach algebra B(E) of bounded operators admits a discontinuous derivation (J. London Math. Soc. 1989). We generalize Read's main theorem about B(E) from which he deduced this conclusion, as well as the key technical lemmas that his proof relied on, by constructing a strongly split-exact sequence{0}→W(E)→B(E)→l2~→{0}, W(E) where W(E) denotes the ideal of weakly compact operators on E, while l2~ is the unitization of the Hilbert space l2, endowed with the zero product.
KW - Bounded operator
KW - Read's Banach space
KW - Banach algebra
KW - short-exact sequence
KW - strong splitting
KW - discontinuous derivation
U2 - 10.4064/sm8554-9-2016
DO - 10.4064/sm8554-9-2016
M3 - Journal article
VL - 236
SP - 51
EP - 62
JO - Studia Mathematica
JF - Studia Mathematica
SN - 0039-3223
ER -