Single and multi-valued Hilbert-bundle renormings

IF 1.2 3区数学 Q1 MATHEMATICS

Annals of Functional Analysis Pub Date : 2025-05-06 DOI:10.1007/s43034-025-00432-6

Alexandru Chirvasitu

引用次数: 0

Abstract

We prove that subhomogeneous continuous Banach bundles over compact metrizable spaces are equivalent to Hilbert bundles, while examples show that the metrizability assumption cannot be dropped completely. This complements the parallel statement for homogeneous bundles without the metrizability assumption, and generalizes the analogous result to the effect that subhomogeneous \(C^*\) bundles over compact metrizable spaces admit finite-index expectations.

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单值和多值hilbert束改造

证明了紧致可度量空间上的次齐次连续Banach束等价于Hilbert束，并举例证明了可度量性假设不能被完全抛弃。这补充了没有度量性假设的齐次束的平行陈述，并推广了类似的结果，即紧化可度量空间上的次齐次束\(C^*\)允许有限指标期望。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Functional Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

10.00%

发文量

期刊介绍： Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory. Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.