Daugavet’s equation and operators on 𝐿¹(𝜇)

Holub, James R.

doi:10.1090/S0002-9939-1987-0884469-8

Daugavet’s equation and operators on $L^ 1(\mu )$
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by James R. Holub

Proc. Amer. Math. Soc. 100 (1987), 295-300

DOI: https://doi.org/10.1090/S0002-9939-1987-0884469-8

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Abstract:

Generalizing a result of Babenko and Pichugov, it is shown that if $T$ is a weakly compact operator on ${L^1}(\mu )$, where $\mu$ is a $\sigma$-finite nonatomic measure, then $\left \| {I + T} \right \| = 1 + \left \| T \right \|$. A characterization of all operators $T$ on ${L^1}(\mu )$ having this property is also given.

References

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