Index o f Notatio n
Generalities
R Th e field o f rea l number s (scalars )
C Th e field o f comple x 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 th e 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 th e se t A
Th e interio r o f th e se t A
co(A) Th e conve x hul l o f th e se t A
co(A) Th e close d conve x hul l o f th e se t A
T : X - » F T i s a surjectiv e linea r operato r
T : X -+ Y T i s a n 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 se t A i n a vecto r 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 Banac h spac e o f al l absolutel y p-summabl e scala r se -
quences: ( { ( A
n
)
n
: Ysn \ Xri\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|| = s u p
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 16
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 16
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 16
X
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