Quotient algebras of Banach operator ideals related to non-classical approximation properties
نویسندگان
چکیده
We investigate the quotient algebra $\mathfrak{A}_X^{\mathcal I}:=\mathcal I(X)/\overline{\mathcal F(X)}^{||\cdot||_{\mathcal I}}$ for Banach operator ideals $\mathcal I$ contained in ideal of compact operators, where $X$ is a space that fails I$-approximation property. The main results concern nilpotent algebras $\mathfrak A_X^{\mathcal{QN}_p}$ and A_X^{\mathcal{SK}_p}$ quasi $p$-nuclear operators $\mathcal{QN}_p$ Sinha-Karn $p$-compact $\mathcal{SK}_p$. include following: (i) if has cotype 2, then A_X^{\mathcal{QN}_p}=\{0\}$ every $p\ge 1$; (ii) $X^*$ A_X^{\mathcal{SK}_p}=\{0\}$ (iii) exact upper bound index nilpotency $p\neq 2$ $\max\{2,\left \lceil p/2 \right \rceil\}$, $\left \rceil$ denotes smallest $n\in\mathbb N$ such $n\ge p/2$; (iv) $p>2$ there closed subspace $X\subset c_0$ both contain countably infinite decreasing chain ideals. In addition, our methods yield compact-by-approximable A_X=\mathcal K(X)/\mathcal A(X)$ contains two incomparable chains
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2023
ISSN: ['0022-247X', '1096-0813']
DOI: https://doi.org/10.1016/j.jmaa.2022.126637