Banach Journal of Mathematical Analysis

Metrization theory and the Kadec property

S. Ferrari, L. Oncina, J. Orihuela, and M. Raja

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Abstract

The uniform structure of a descriptive normed space (X,) always admits a description with an (F)-norm 1 such that weak and norm topologies coincide on

{xX:x1=ρ} for every ρ>0.

Article information

Source
Banach J. Math. Anal., Volume 10, Number 2 (2016), 281-306.

Dates
Received: 7 November 2014
Accepted: 2 June 2015
First available in Project Euclid: 15 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1458053863

Digital Object Identifier
doi:10.1215/17358787-3492809

Mathematical Reviews number (MathSciNet)
MR3474840

Zentralblatt MATH identifier
1351.46002

Subjects
Primary: 46A16: Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
Secondary: 46B03: Isomorphic theory (including renorming) of Banach spaces 46B20: Geometry and structure of normed linear spaces 46B26: Nonseparable Banach spaces 54E35: Metric spaces, metrizability

Keywords
quasinorm ($F$)-norm Kadec norm descriptive Banach space network $p$-convexity

Citation

Ferrari, S.; Oncina, L.; Orihuela, J.; Raja, M. Metrization theory and the Kadec property. Banach J. Math. Anal. 10 (2016), no. 2, 281--306. doi:10.1215/17358787-3492809. https://projecteuclid.org/euclid.bjma/1458053863


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