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A counterexample in the theory of Hermitian liftings

Published online by Cambridge University Press:  20 January 2009

D. A. Legg
D. A. Legg
Affiliation:
Department of Mathematics, Indiana University, Purdue University at Fort Wayne, Fort Wayne, In 46805
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In [3], [8], and [2], it was shown that if is an essentially Hermitian operator on l P, 1≦ p<∞, or on Lp[0,1], 1< p<∞, then T is a compact perturbation of a Hermitian operator. In [1], this result was established for operators on Orlicz sequence space l M, where 2∉[α M,β M] (the associated interval for M). In that same paper, it was conjectured that this result does not in general hold if 2∈[α M,β M]. In this paper, we show that this conjecture is correct by exhibiting an Orlicz sequence space l M and an essentially Hermitian operator on l M which is not a compact perturbation of a Hermitian operator.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 25 , Issue 2 , June 1982 , pp. 141 - 144
Copyright
Copyright © Edinburgh Mathematical Society 1982

References

REFERENCES

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