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PreprintCC BY 4.0arXiv

The Subnormality of 𝕂-Homogeneous Multiplication Operators on Bounded Symmetric Domains

  • Surjit Kumar
  • Milan Kumar Mal
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Abstract

Let Ω=G/𝕂 be an irreducible bounded symmetric domain of rank r and dimension d. In this paper, we study the joint subnormality of d-tuple of multiplication operators induced by the coordinate functions on reproducing kernel Hilbert spaces of holomorphic functions on Ω determined by 𝕂-invariant kernels. We introduce the notion of contractive d-tuple associated with Ω and prove that the weighted Bergman shifts on Ω are contractive d-tuple precisely when they are jointly subnormal. A characterization of joint subnormality further leads to the study of a class of moment problems, which we refer to as twisted moment problems. We establish that the twisted moment problem is equivalent to an appropriate Hausdorff moment problem. This equivalence provides a moment-theoretic characterization of joint subnormality for the multiplication operators under consideration.

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Cite

BibTeXRIS
BibTeX
@misc{kumar2026subnormality,
  title = {{The Subnormality of $\mathbb K$-Homogeneous Multiplication Operators on Bounded Symmetric Domains}},
  author = {Surjit Kumar and Milan Kumar Mal},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26434},
  eprint = {2609.26434},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26434},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Subnormality of 𝕂-Homogeneous Multiplication Operators on Bounded Symmetric Domains
AU  - Surjit Kumar
AU  - Milan Kumar Mal
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26434
UR  - https://arxiv.org/abs/2609.26434
AB  - Let Ω=G/𝕂 be an irreducible bounded symmetric domain of rank r and dimension d. In this paper, we study the joint subnormality of d-tuple of multiplication operators induced by the coordinate functions on reproducing kernel Hilbert spaces of holomorphic functions on Ω determined by 𝕂-invariant kernels. We introduce the notion of contractive d-tuple associated with Ω and prove that the weighted Bergman shifts on Ω are contractive d-tuple precisely when they are jointly subnormal. A characterization of joint subnormality further leads to the study of a class of moment problems, which we refer to as twisted moment problems. We establish that the twisted moment problem is equivalent to an appropriate Hausdorff moment problem. This equivalence provides a moment-theoretic characterization of joint subnormality for the multiplication operators under consideration.
ER  -