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- W2070030118 abstract "Let E be a real or complex n -dimensional normed space. Deschaseaux (1) has shown that if the absolutely summing constant π 1 ( E ) = n then E is isometrically isomorphic to . (For the definition of π 1 ( E ) and related quantities, see (2).) It is well-known ((3), (4) and (6)) that if E is a P 1 -space then E is isometrically isomorphic to . We shall show that Deschaseaux' result follows easily from this, and from the following elementary result: Proposition. If S is a linear operator on a real or complex n-dimensional normed space E, then |trace S| ≤ ‖S‖, with equality if and only if S is a scalar multiple of the identity I." @default.
- W2070030118 created "2016-06-24" @default.
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- W2070030118 date "1974-09-01" @default.
- W2070030118 modified "2023-09-28" @default.
- W2070030118 title "Operators with large trace, and a characterization of" @default.
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- W2070030118 doi "https://doi.org/10.1017/s0305004100049094" @default.
- W2070030118 hasPublicationYear "1974" @default.
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