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- W2247689057 abstract "For any measurable set E of a measure space (X,μ), let PE be the (orthogonal) projection on the Hilbert space L2(X,μ) with the range ranPE={f∈L2(X,μ):f=0a.e. onEc} that is called a standard subspace of L2(X,μ). Let T be an operator on L2(X,μ) having increasing spectrum relative to standard compressions, that is, for any measurable sets E and F with E⊆F, the spectrum of the operator PET|ranPE is contained in the spectrum of the operator PFT|ranPF. In 2009, Marcoux, Mastnak and Radjavi asked whether the operator T has a non-trivial invariant standard subspace. They answered this question affirmatively when either the measure space (X,μ) is discrete or the operator T has finite rank. We study this problem in the case of trace-class kernel operators. We also slightly strengthen the above-mentioned result for finite-rank operators." @default.
- W2247689057 created "2016-06-24" @default.
- W2247689057 creator A5060575349 @default.
- W2247689057 date "2017-03-01" @default.
- W2247689057 modified "2023-10-16" @default.
- W2247689057 title "Triangularizability of trace-class operators with increasing spectrum" @default.
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- W2247689057 doi "https://doi.org/10.1016/j.jmaa.2016.10.066" @default.
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