Duals of spaces of operators

Hi all,

We have the following chain of isometric isomorphisms

c_0^* = l^1
(B) l^1^* = l^\infty

where c_0 is the Banach space of sequences converging to 0, * is the
dual functor, l^1 is the space of summable sequences and l^\infty the
space of bounded sequences.

Similarly, we have the chain of isometric isomorphisms

K^* = T
(A) T^* = B

where K is the space of compact operators H -> H with H a Hilbert
space, T is the space of trace class operators and B the space of
bounded operators.

My question is, does there exist a similar result with H a Banach
space? Something like (B) with T the space of absolutely summing
operators or whatever-operators? In other words, is the space of
bounded operators A -> B a dual Banach space (itself a dual Banach
space)? And assuming the answer is yes, is the proof similar (for some
unspecified value of "similar") to the Hilbert space case?

Best regards,
G. Rodrigues
.

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