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pro vyhledávání: '"Oikhberg, T."'
Let $(\Omega,\Sigma,\mu)$ be a measure space, and $1\leq p\leq \infty$. A subspace $E\subseteq L_p(\mu)$ is said to do stable phase retrieval (SPR) if there exists a constant $C\geq 1$ such that for any $f,g\in E$ we have $$ \inf_{|\lambda|=1} \|f-\l
Externí odkaz:
http://arxiv.org/abs/2210.05114
We investigate the structure of the free $p$-convex Banach lattice $FBL^{(p)}[E]$ over a Banach space $E$. After recalling why such a free lattice exists, and giving a convenient functional representation of it, we focus our study on how properties o
Externí odkaz:
http://arxiv.org/abs/2210.00614
Autor:
Helemskii, A. Ya., Oikhberg, T.
The paper investigates free and projective ${\bf L}$-spaces, where ${\bf L}$ is a given normed space. These spaces form a far-reaching generalization of known $p$-multinormed spaces; in particular, if ${\bf L}=L_p(X)$, the ${\bf L}$-spaces can be con
Externí odkaz:
http://arxiv.org/abs/2109.01786
Autor:
Oikhberg, T.
Publikováno v:
In Journal of Functional Analysis 15 April 2024 286(8)
Akademický článek
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Autor:
Oikhberg, T.1 (AUTHOR) oikhberg@illinois.edu, Tursi, M. A.2 (AUTHOR)
Publikováno v:
Banach Journal of Mathematical Analysis. Oct2024, Vol. 18 Issue 4, p1-28. 28p.
We investigate various aspects of the "weighted" greedy algorithm with respect to a Schauder basis. For a weight w, we describe w-greedy, w-almost-greedy and w-partially-greedy bases, and show some properties of w-semi-greedy bases. To achieve these
Externí odkaz:
http://arxiv.org/abs/1803.05052
We obtain Lebesgue-type inequalities for the greedy algorithm for arbitrary complete seminormalized biorthogonal systems in Banach spaces. The bounds are given only in terms of the upper democracy functions of the basis and its dual. We also show tha
Externí odkaz:
http://arxiv.org/abs/1707.07513
Publikováno v:
Mathematische Annalen; Sep2024, Vol. 390 Issue 1, p1-43, 43p
Publikováno v:
In Journal of Approximation Theory December 2019 248