Index o f Notatio n Generalities R Th e field o f real number s (scalars ) C Th e field o f complex number s (scalars ) K Th e generi c scala r field R o r C M.n Th e n-dimensional Euclidea n spac e T^(E) Th e invers e imag e o f the se t E unde r th e operato r T ker(T) Th e kerne l o f T (=T« - ({0})) A Th e closur e o f the se t A Th e interio r o f the se t A co(A) Th e conve x hul l o f the se t A co(A) Th e close d conve x hul l o f the se t A T : X - » F T i s a surjective linea r operato r T : X -+ Y T i s an injectiv e linea r operato r F{X) Th e se t o f al l finite dimensiona l subspace s o f th e Banac h space X Bx Th e uni t bal l o f a Banac h spac e X idx Th e identit y operato r o n th e vecto r spac e X exiA Th e se t o f al l extrem e point s o f a set A i n a vector spac e XA Th e indicato r o r characteristi c functio n o f A rn(-) Th e n-t h Rademache r functio n define d o n [0,1] : rn(t) sign ( sin 2n7rt) Vector spaces Banac h space s Xf Th e algebraic dua l o f a vecto r spac e X X* Th e (continuous ) dua l o f a Banac h spac e £p Th e Banach spac e o f al l absolutel y p-summabl e scala r se - quences: ( {(A n ) n : Ysn \ X ri\p oo}) l l ( A n ) n | | = ( E n | A n | P ) " £°° Th e Banac h spac e o f al l bounde d scala r sequences ||(An)n|| =sup n |A n | Co Th e Banac h spac e o f al l scala r nul l sequences ||(A n )n|| = SUp n |A n | Px o r £ P (X) Th e Banac h spac e o f al l absolutel y p-summabl e sequence s 1 6 in a Banac h spac e X £^ o r £°°(X) Th e Banac h spac e o f al l bounde d sequence s i n a Banac h 1 6 space X CQ{X) Th e Banac h spac e o f al l nul l sequence s i n a Banac h spac e 1 6 X 273
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