Abstract
In this note we study some spectral properties of a class of operators. Denote by I the closed interval [0,1] and by LP the usual Banach space of (equivalence classes coof) measurable functions on I with integrable p-th power for p ɛ [1, ∞), while L∞ stands for the space of essentially bounded functions. We use the ordinary Lebesgue measure in all these definitions. Furthermore, denote by C the Banach space of continuous functions on I with the supremum norm. Note that the space C can be regarded as a closed subspace of L∞. In what follows, the symbol X will stand either for some of the spaces LP with p ɛ [1,∞], or for the space C, unless stated otherwise.
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© 1986 Springer Basel AG
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Omladič, M. (1986). Some Spectral Properties of an Operator. In: Douglas, R.G., Pearcy, C.M., Sz.-Nagy, B., Vasilescu, FH., Voiculescu, D., Arsene, G. (eds) Advances in Invariant Subspaces and Other Results of Operator Theory. Operator Theory: Advances and Applications, vol 17. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7698-8_19
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