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The purpose of this note is te give an explicit construction of a bounded operator T acting en the Space L2[0,1] such that T f(x) j < fo f(y)(dy for a.e . x E [0,11 and, nevertheless, JITIls, = oo for every p < 2. Here 11 ~Isp denotes the norm associated te the Schatten-von Neumann classesdoi:10.5565/publmat_37293_07 fatcat:kblrth2envgy7kpzxvh4tu5pqi