Essentially Hermitian operators in 𝐵(𝐿_{𝑝})

Allen, G. D.; Legg, D. A.; Ward, J. D.

doi:10.1090/S0002-9939-1980-0574511-X

Essentially Hermitian operators in $B(L_{p})$
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by G. D. Allen, D. A. Legg and J. D. Ward PDF

Proc. Amer. Math. Soc. 80 (1980), 71-77 Request permission

Abstract:

It is shown that on ${L_p}[0,1]$ all bounded linear operators which are Hermitian in the Calkin algebra $B({L_p})/C({L_p})$, must be of the form “Hermitian plus compact". That is, essentially Hermitian operators have the form, real multiplier plus compact.

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