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Taylor-type joint spectrum and essential spectrum of row-bounded sequences of commuting operators
Abstract
As the cornerstone of multivariable operator theory, (essential) Taylor's joint spectrum plays crucial roles in many areas. The present paper is devoted to developing the theory of (essential) Taylor-type joint spectrum of row-bounded sequences of commuting operators on Hilbert spaces and to establishing the associated Fredholm index theory. Furthermore, the holomorphic functional calculus for row-bounded sequences is established. At last, we obtain a Gleason-Richter-Sundberg type index theorem in the infinite-variable setting, which connects the Fredholm index, the asymptotic Arveson's curvature invariant and fibre dimensions.
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BibTeX
@misc{wang2026taylortype,
title = {{Taylor-type joint spectrum and essential spectrum of row-bounded sequences of commuting operators}},
author = {Penghui Wang and Fan Zhang and Ruoyu Zhang and Zeyou Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41882},
eprint = {2610.41882},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41882},
}
RIS
TY - UNPB
TI - Taylor-type joint spectrum and essential spectrum of row-bounded sequences of commuting operators
AU - Penghui Wang
AU - Fan Zhang
AU - Ruoyu Zhang
AU - Zeyou Zhu
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41882
UR - https://arxiv.org/abs/2610.41882
AB - As the cornerstone of multivariable operator theory, (essential) Taylor's joint spectrum plays crucial roles in many areas. The present paper is devoted to developing the theory of (essential) Taylor-type joint spectrum of row-bounded sequences of commuting operators on Hilbert spaces and to establishing the associated Fredholm index theory. Furthermore, the holomorphic functional calculus for row-bounded sequences is established. At last, we obtain a Gleason-Richter-Sundberg type index theorem in the infinite-variable setting, which connects the Fredholm index, the asymptotic Arveson's curvature invariant and fibre dimensions.
ER -