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Sneh Lata,
Sushant Pokhriyal, and
Dinesh Singh
Invariant subspaces of powers of some unicellular operators
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| Published: |
February 23, 2023. |
| Keywords: |
Invariant subspace, Unicellular operators, weighted shifts, Joint-invariant subspace. |
| Subject [2010]: |
Primary 47A15; Secondary 47B02, 47B37. |
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Abstract
We study subspaces which are invariant under squares and cubes (separately as well as jointly) of unicellular backward weighted shift operators on a separable Hilbert space. The finite-dimensional subspaces are characterized for all weights and the infinite-dimensional subspaces are characterized for two classes of weights.
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| Acknowledgements
The authors thank the referee for the comments that improved the presentation and removed typos. The first and third authors also thank the Mathematical Sciences Foundation, Delhi for support and facilities needed to complete the present work. The research of the first author is supported by the Mathematical Research Impact Centric Support (MATRICS) grant, File No: MTR/2017/000749, by the Science and Engineering Research Board (SERB), Department of Science & Technology (DST), Government of India.
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| Author information
Sneh Lata:
Department Of Mathematics
Shiv Nadar University
School of Natural Sciences
Gautam Budh Nagar - 203207, Uttar Pradesh, India
sneh.lata@snu.edu.in
Sushant Pokhriyal:
Department Of Mathematics
Shiv Nadar University
School of Natural Sciences
Gautam Budh Nagar - 203207, Uttar Pradesh, India
sp259@snu.edu.in
Dinesh Singh:
Centre For Lateral Innovation, Creativity and Knowledge
SGT University
Gurugram 122505, Haryana, India
dineshsingh1@gmail.com
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