Abstract.
Let denote the von Neumann–Schatten class, its norm and let be an elementary operator defined by . We shall characterize those operators which are orthogonal to the range of in the sense that for all . The main results of this paper are: If and (i) if A, C, respectively B, D are commuting normal operators with , or (ii) if A, B are contractions and , then is orthogonal to the range of if and only of S is in the kernel of . Furthermore, in both cases, the algebraic direct sum satisfies .
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(Received 9 February 2000; in revised form 21 February, 2001)
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Turnšek, A. Orthogonality in Classes. Mh Math 132, 349–354 (2001). https://doi.org/10.1007/s006050170039
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DOI: https://doi.org/10.1007/s006050170039