PreprintarXiv licencearXiv
Soft normed linear spaces via soft elements: decomposition, convergence, and operators
Abstract
Let F: A→𝒫(X) be a soft linear subspace of a linear space X over 𝕂. Its soft elements form the product ∏t∈ AF(t). We use this representation to characterize selection spaces, decompose soft norms and soft linear operators into their sectionwise parts, and compare soft, uniform, and componentwise convergence. We also characterize completeness and continuity in the box, extended-supremum, and product settings. Neumann-series and fixed-point results are obtained as applications.
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BibTeX
@misc{ray2026soft,
title = {{Soft normed linear spaces via soft elements: decomposition, convergence, and operators}},
author = {Subhasis Ray},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35879},
eprint = {2610.35879},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35879},
}
RIS
TY - UNPB
TI - Soft normed linear spaces via soft elements: decomposition, convergence, and operators
AU - Subhasis Ray
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.35879
UR - https://arxiv.org/abs/2610.35879
AB - Let F: A→𝒫(X) be a soft linear subspace of a linear space X over 𝕂. Its soft elements form the product ∏_t∈ AF(t). We use this representation to characterize selection spaces, decompose soft norms and soft linear operators into their sectionwise parts, and compare soft, uniform, and componentwise convergence. We also characterize completeness and continuity in the box, extended-supremum, and product settings. Neumann-series and fixed-point results are obtained as applications.
ER -