ON ASYMPTOTIC PROPERTIES OF POSITIVE OPERATORS ON BANACH LATTICES
Bibliographic record
Abstract
In this thesis, we study two problems. The first one is the renorming problem in Banach lattices. We state the problem and give some known results related to it. Then we pass to construct a positive doubly power bounded operator with a nonpositive inverse on an infinite dimensional AL-space which generalizes the result of [10]. The second problem is related to the mean ergodicity of positive operators on KBspaces. We prove that any positive power bounded operator T in a KB-space E which satisfies lim n!1 dist 1 n n1 Xk=0 Tkx, [g, g] + BE = 0 (8x 2 E, kxk 1), ( ) where BE is the unit ball of E, g 2 E+, and 0 < 1, is mean ergodic and its fixed space Fix(T) is finite dimensional. This generalizes the main result of [12]. Moreover, under the assumption that E is a -Dedekind complete Banach lattice, we prove that if, for any positive power bounded operator T, the condition ( ) implies that T is mean ergodic then E is a KB-space.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.019 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".