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Monojit Bhattacharjee,
Rajeev Gupta, and
Vidhya Venugopal
Wold-type decomposition for doubly commuting two-isometries
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| Published: |
August 25, 2026. |
| Keywords: |
m-isometry, m-concave operators, wandering subspace property, Wold-type decomposition, Dirichlet-type spaces. |
| Subject [2020]: |
Primary 46E20, 47B32, 47B38, Secondary 47A50, 31C25. |
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Abstract
In this article, we prove that any pair of doubly commuting 2-isometries on a Hilbert space has a Wold-type decomposition. Moreover, the analytic part of the pair is unitary equivalent to the pair of multiplication by the coordinate functions on a Dirichlet-type space on the bidisc.
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| Acknowledgements
The first named author's research is supported by the DST-INSPIRE Faculty Grant with Fellowship No. DST/INSPIRE/04/2020/001250 and the third named author's research work is supported by the BITS Pilani institute fellowship.
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| Author information
Monojit Bhattacharjee
Department of Mathematics
Birla Institute of Technology and Science
K K Birla Goa Campus, India
monojitb@goa.bits-pilani.ac.in
Rajeev Gupta
School of Mathematics and Computer Science
Indian Institute of Technology Goa, India
rajeev@iitgoa.ac.in
Vidhya Venugopal
Department of Mathematics
Birla Institute of Technology and Science
K K Birla Goa Campus, India
p20200024@goa.bits-pilani.ac.in
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