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arXiv · 2610.02919

Spectral Properties of Convolution Operators on Non-Separable Sequence Spaces

Sayan Saha·Arnab Patra
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Abstract

This paper provides a complete characterization of the spectrum, point spectrum, continuous spectrum, and residual spectrum of bounded convolution operators acting on the non-separable space $σ_\infty$, the dual of the Hahn sequence space. Because standard duality and separability-based techniques fail in this setting, a linear functional approach is employed with the fine spectral decomposition of the unilateral shift operator. Furthermore, as a major application of this methodology, we establish a complete description of the fine spectrum for operator polynomials acting on general sequence spaces without requiring separability. This result provides a unified framework that subsumes classical spectral determinations for general banded triangular matrices across various sequence spaces and enables the explicit computation of fine spectrum on non-separable spaces.

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BibTeXRIS

Sayan Saha, Arnab Patra. 2026-10-02. Spectral Properties of Convolution Operators on Non-Separable Sequence Spaces. https://arxiv.org/abs/2610.02919

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