274 Cak W Cm uc(X) C(K) t°°(Bx*) INDEX O F NOTATIO N The Banac h spac e o f weakl y p-summabl e sequence s i n a Banach spac e X The subspac e o f ^eak(^)' consistin g o f al l sequence s (x n ) of vectors i n X, suc h that : linin^oo 11(0 , ...,0,xn,z n +i,...)||*p e a k = 0 The Banac h spac e o f al l unconditionall y summabl e se - quences i n a Banac h spac e X thi s i s th e sam e Banac h space a s ^ W eakP0 The Banac h spac e o f al l Bochne r integrabl e function s de - fined on some measure space (Q, /i) with values in a Banach space X \\f\\ L ix{fJL) = / ||/||xd/ i The Banac h spac e of all Bochner p-integrable function s de - fined o n some measure space (fi , /i) with values in a Banach space* | | / | | L * w = (/||/|&d/x) ' The Banac h spac e o f al l continuou s function s define d o n a compact se t K 16 16 18 172 173 Spaces o f linea r an d bilinea r function s L(X Y) Th e spac e o f al l linea r function s / : X » Y X , Y vecto r 2 spaces B(X, Y Z) Th e spac e o f all bilinear function s p : X x Y - » Z X , Y, Z 1 vector space s B(X, Y) Th e spac e o f all bilinear functional s (forms ) o n ! x 7 1 C(X\ Y) Th e space of all bounded linea r operators T : X Y X, Y Banach space s £(X, Y Z) Th e Banac h spac e o f al l bounde d bilinea r operator s ip : 7 X x Y ^ Z X , Y, Z Banac h psace s B(X, Y) Th e Banac h spac e o f all bounded bilinea r form s o n X x Y 7 X, Y Banac h space s JT(X Y) Th e spac e o f al l bounde d linea r operator s T : X Y o f finite ran k /C(X Y) Th e spac e o f al l compact linea r operator s T : X ^ Y W(X Y) Th e spac e o f al l weakly compac t linea r operator s T : X Y ®(#) Th e C*-algebr a o f all bounded linea r operator s T : H -* H defined o n a Hilbert spac e H IC(H) Th e spac e o f al l compac t linea r operator s T : H H defined o n a Hilbert spac e H Ca(X Y ) Th e spac e o f al l a-integral operator s (operator s o f type a) 4 7 || ||c Th e a- integral operato r nor m 4 7 £ a (X Y) Th e spac e o f al l a-nuclea r operator s 5 4 Na Th e a-nuclea r operato r nor m 5 4 Ba{X, Y) Th e spac e o f bilinea r functional s o f typ e a o r a-integra l 3 2 bilinear form s Ba (X , Y) Th e spac e o f a-nuclear bilinea r form s 5 4
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