Factorisation in stopping-time Banach spaces: Identifying unique maximal ideals
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00561242" target="_blank" >RIV/67985840:_____/22:00561242 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.aim.2022.108643" target="_blank" >https://doi.org/10.1016/j.aim.2022.108643</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aim.2022.108643" target="_blank" >10.1016/j.aim.2022.108643</a>
Alternative languages
Result language
angličtina
Original language name
Factorisation in stopping-time Banach spaces: Identifying unique maximal ideals
Original language description
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.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Advances in Mathematics
ISSN
0001-8708
e-ISSN
1090-2082
Volume of the periodical
409
Issue of the periodical within the volume
November 19
Country of publishing house
US - UNITED STATES
Number of pages
35
Pages from-to
108643
UT code for WoS article
000878859700003
EID of the result in the Scopus database
2-s2.0-85137109918