Factorisation in stopping-time Banach spaces: Identifying unique maximal ideals

0561242 - MÚ 2023 RIV US eng J - Článek v odborném periodiku
Kania, Tomasz - Lechner, R.
Factorisation in stopping-time Banach spaces: Identifying unique maximal ideals.
Advances in Mathematics. Roč. 409, November 19 (2022), č. článku 108643. ISSN 0001-8708. E-ISSN 1090-2082
Institucionální podpora: RVO:67985840
Klíčová slova: factorisation * primarity * stopping-time Banach spaces * unique maximal operator ideals
Obor OECD: Pure mathematics
Impakt faktor: 1.7, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1016/j.aim.2022.108643

Stopping-time Banach spaces is a collective term for the class of spaces of eventually null integrable processes that are defined in terms of the behaviour of the stopping times with respect to some fixed filtration. From the point of view of Banach space theory, these spaces in many regards resemble the classical spaces such as L1 or C(Δ), but unlike these, they do have unconditional bases. In the present paper, we study the canonical bases in the stopping-time spaces in relation to factorising the identity operator thereon. Since we work exclusively with the dyadic-tree filtration, this setup enables us to work with tree-indexed bases rather than directly with stochastic processes. En route to the factorisation results, we develop general criteria that allow one to deduce the uniqueness of the maximal ideal in the algebra of operators on a Banach space. These criteria are applicable to many classical Banach spaces such as (mixed-norm) Lp-spaces, BMO, SL∞, and others.
Trvalý link: https://hdl.handle.net/11104/0333925