CrossRef Open Access 2023

Automatic continuity of separating and biseparating isomorphisms

Ching-on Lo Anthony Loh

Abstrak

Let p p be a fixed number with 1 ≤ p > ∞ 1 \leq p > \infty . It is shown that every surjective and biseparating linear map between L p L^p -spaces is continuous when the underlying measure space is non-atomic. We also prove that a separating isomorphism on l p l^p is both continuous and biseparating. Furthermore, these (bi-)separating maps take the form of a weighted composition operator. Our proofs are direct, elementary and do not invoke deep results about Riesz spaces or Banach lattices.

Penulis (2)

Ching-on Lo

Anthony Loh

Format Sitasi

APA MLA BibTeX

Lo, C., Loh, A. (2023). Automatic continuity of separating and biseparating isomorphisms. https://doi.org/10.1090/proc/16210

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Informasi Jurnal

Tahun Terbit: 2023
Bahasa: en
Sumber Database: CrossRef
DOI: 10.1090/proc/16210
Akses: Open Access ✓