کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5775145 | 1413576 | 2017 | 14 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Triangularizability of trace-class operators with increasing spectrum
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
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={fâL2(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 EâF, 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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 447, Issue 2, 15 March 2017, Pages 1102-1115
Journal: Journal of Mathematical Analysis and Applications - Volume 447, Issue 2, 15 March 2017, Pages 1102-1115
نویسندگان
Roman Drnovšek,