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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Essentially Hermitian operators in $ B(L\sb{p})$


Authors: G. D. Allen, D. A. Legg and J. D. Ward
Journal: Proc. Amer. Math. Soc. 80 (1980), 71-77
MSC: Primary 47B15
MathSciNet review: 574511
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0574511-X
PII: S 0002-9939(1980)0574511-X
Article copyright: © Copyright 1980 American Mathematical Society