Thorp has shown that for X
and Y certain Banach spaces of sequences there is no continuous linear projection of
the bounded linear operators from X to Y onto the compact linear operators
from X to Y . In this paper, this result, as well as related results for the
weakly compact linear operators, is demonstrated for cases including (a)
X an infinite dimensional abstract L-space and Y an infinite dimensional
space whose conjugate contains a countable total set and (b) X a separable
B-space and Y = C(S) with S either a metric space containing an infinite
number of points or S a compact space which contains a one-to-one convergent
sequence.
