Lacunary Power Sequences and Extremal Vectors
| Main Author: | |
|---|---|
| Language: | English |
| Published: |
Kent State University / OhioLINK
2008
|
| Subjects: | |
| Online Access: | http://rave.ohiolink.edu/etdc/view?acc_num=kent1216064259 |
| id |
ndltd-OhioLink-oai-etd.ohiolink.edu-kent1216064259 |
|---|---|
| record_format |
oai_dc |
| spelling |
ndltd-OhioLink-oai-etd.ohiolink.edu-kent12160642592021-08-03T05:36:32Z Lacunary Power Sequences and Extremal Vectors Fenta, Aderaw Workneh Mathematics Schauder basis Basic sequence Lacunary sequence Extremal vectr Backward minimal vector Rectifiable curve <p> This dissertation has two parts. The first four chapters deal with lacunary power sequences. In 1966, V.I. Gurariy and V.I. Matsaev showed that a sequence {t<sup>λ<sub>k</sub></sup>} is a basic sequence in the spaces C[0, 1] and L<sub>p</sub>[0, 1], (1 ≤ p < ∞) if and only if {λ<sub>k</sub>} is a lacunary sequence. Here, we use various methods to generalize this result to sequences {h<sup>λ<sub>k</sub></sup>f} in the spaces C[a, b] and L<sub>p</sub>[a, b], where 1 ≤ p < ∞ and 0 ≤ a < b.</p> <p>The fifth chapter is on extremal vectors. In 1996 P. Enflo introduced backward minimal vectors to study invariant subspaces. If a bounded linear operator T on a Hilbert space H has dense range, then for each non-zero element x<sub>0</sub> of H, each positive number epsilon; with ε ≤ ‖x<sub>0</sub>‖ and each natural number n, there exists a unique vector y<sub>ε</sub> = y(x<sub>0</sub> , ε , n), called backward minimal vector, such that ‖T<sup>n</sup>y<sub>ε</sub> - x<sub>0</sub>‖ ≤ ε and y = inf{‖y‖ : ‖T<sup>n</sup>y - x<sub>0</sub>‖ ≤ ε}. Here, we investigate rectifiability properties of the curve γ : ε → Ty<sub>ε</sub> for the multiplication operator T on L<sub>2</sub>[0, 1]. </p> 2008-07-15 English text Kent State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=kent1216064259 http://rave.ohiolink.edu/etdc/view?acc_num=kent1216064259 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws. |
| collection |
NDLTD |
| language |
English |
| sources |
NDLTD |
| topic |
Mathematics Schauder basis Basic sequence Lacunary sequence Extremal vectr Backward minimal vector Rectifiable curve |
| spellingShingle |
Mathematics Schauder basis Basic sequence Lacunary sequence Extremal vectr Backward minimal vector Rectifiable curve Fenta, Aderaw Workneh Lacunary Power Sequences and Extremal Vectors |
| author |
Fenta, Aderaw Workneh |
| author_facet |
Fenta, Aderaw Workneh |
| author_sort |
Fenta, Aderaw Workneh |
| title |
Lacunary Power Sequences and Extremal Vectors |
| title_short |
Lacunary Power Sequences and Extremal Vectors |
| title_full |
Lacunary Power Sequences and Extremal Vectors |
| title_fullStr |
Lacunary Power Sequences and Extremal Vectors |
| title_full_unstemmed |
Lacunary Power Sequences and Extremal Vectors |
| title_sort |
lacunary power sequences and extremal vectors |
| publisher |
Kent State University / OhioLINK |
| publishDate |
2008 |
| url |
http://rave.ohiolink.edu/etdc/view?acc_num=kent1216064259 |
| work_keys_str_mv |
AT fentaaderawworkneh lacunarypowersequencesandextremalvectors |
| _version_ |
1719422448244359168 |