arXiv subjects

Thanatkrit Kaewtem

Publications and source records attributed to Thanatkrit Kaewtem.

2 recordsLinked to original sources

arXiv2021

Entropy numbers of diagonal operators on Orlicz sequence spaces

Let $M_1$ and $M_2$ be functions on $[0,1]$ such that $M_1(t^{1/p})$ and $M_2(t^{1/p})$ are Orlicz functions for some $p \in (0,1].$ Assume that $M_2^{-1} (1/t)/M_1^{-1} (1/t)$ is non-decreasing for $t \geq 1.$ Let $(α_i)_{i=1}^\infty$ be a non-increasing sequence of non-negative real numbers. Under some conditions on $(α_i)_{i=1}^\infty,$ sharp two-sided estimates for entropy numbers of diagonal operators $T_α:\ell_{M_1} \rightarrow \ell_{M_2}$ generated by $(α_i)_{i=1}^\infty,$ where $\ell_{M_1}$ and $\ell_{M_2}$ are Orlicz sequence spaces, are proved. The results generalise some works of Edmunds and Netrusov and hence a result of Cobos, Kühn and Schonbek.

math.FA↗

arXiv2017

Entropy numbers in $γ$-Banach spaces

Let $X$ be a quasi-Banach space, $Y$ a $γ$-Banach space $(0<γ\leq 1)$ and $T$ a bounded linear operator from $X$ into $Y$. In this paper, we prove that the first outer entropy number of $T$ lies between $2^{1-1/γ}\|T\|$ and $\|T\|$; more precisely, $2^{1-1/γ}\|T\| \leq e_1(T) \leq \|T\|,$ and the constant $2^{1-1/γ}$ is sharp. Moreover, we show that there exist a Banach space $X_0$, a $γ$-Banach space $Y_0$ and a bounded linear operator $T_0:X_0 \rightarrow Y_0$ such that $0 \neq e_k(T_0) = 2^{1-1/γ}\|T_0\| $ for all positive integers $k.$ Finally, the paper also provides two-sided estimates for entropy numbers of embeddings between finite dimensional symmetric $γ$-Banach spaces.

math.FA↗