Year: 2026
Type: article
Abstract: Every bounded operator T : E → Y from a Banach lattice E into a Banach space Y admits a canonical localisation on the order-continuous ideal E a .A band BT ⊆ E a is introduced as the largest band of E a on which T is AM-compact.Equivalently, an element x ∈ E a belongs to BT precisely when T ([-|x|, |x|]) is relatively compact in Y .This order-interval compactness is quantified by a lattice seminorm µT on E a , defined via the Kuratowski measure of noncompactness of T ([-|x|, |x|]).The kernel of µT coincides with BT , thereby establishing a link with the restriction characterisation for LW-compact operators.
Source: Contributions to Mathematics
DOI: 10.47443/cm.2025.120
Institution: Manipur University
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: University Grants Commission
OpenAlex ID: W7124978852
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