AI 中文总结
该研究受弱极大性质启发，提出弱p-奇异极大性质，刻画了相关序列空间的奇异极大性质、Schur性质，推导了通用范数可达性的刻画及p-收敛扰动性质与奇异极大性质的关系。
AI 中文摘要
受弱极大性质（WMP）的启发，我们研究了有界线性算子极大序列的p-可和性条件。由于朴素的p-可和性表述与p无关，且对所有算子均退化为范数可达性，我们引入了弱p-奇异极大性质（SMPₚ），其基于不存在弱p-可和子序列的极大序列。我们完全刻画了对(p, q)和(p, c₀)具有SMPᵣ的情况，揭示了其与WMP的显著差异。我们还通过WMP和SMPᵣ刻画了p阶Schur性质。在相对弱p-预紧性和适当的邓福德-佩蒂斯型假设下，我们通过伴随算子的SMP_q或弱*到弱*极大性质，刻画了从X到Y的算子的通用范数可达性，并推导了SMPₚ对应的对偶结果。最后，我们引入算子及其伴随的p-收敛扰动性质，对经典序列空间刻画了该性质，并证明p-收敛扰动性质严格弱于SMPₚ。
英文摘要
Motivated by the weak maximizing property ($\mathrm{WMP}$), we investigate $p$-summability conditions on maximizing sequences of bounded linear operators. Since the naive $p$-summability formulation is independent of $p$ and collapses to norm attainment for all operators, we introduce the weakly $p$-singular maximizing property ($\mathrm{SMP}_p$), based on maximizing sequences with no weakly $p$-summable subsequence. We completely characterize when the pairs $(\ell_p,\ell_q)$ and $(\ell_p,c_0)$ have the $\mathrm{SMP}_r$, revealing sharp contrasts with the $\mathrm{WMP}$. We also characterize the Schur property of order $p$ via the $\mathrm{WMP}$ and the $\mathrm{SMP}_r$. Under relative weak $p$-precompactness and suitable Dunford-Pettis-type assumptions, we characterize universal norm attainment for operators from $X$ to $Y$ in terms of either the $\mathrm{SMP}_q$ for adjoint operators or the weak$^{*}$-to-weak$^{*}$ maximizing property, and derive corresponding duality consequences for the $\mathrm{SMP}_p$. Finally, we introduce $p$-convergent perturbation properties for operators and their adjoints, characterize them for classical sequence spaces, and show that the $p$-convergent perturbation property is strictly weaker than the $\mathrm{SMP}_p$.
Comments19 pages
